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Addressing personal protective equipment (PPE) decontamination: Methylene blue and light inactivates severe acute respiratory coronavirus virus 2 (SARS-CoV-2) on N95 respirators and medical masks with maintenance of integrity and fit
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- Thomas Sean Lendvay, James Chen, Brian H. Harcourt, Florine E. M. Scholte, Ying Ling Lin, F. Selcen Kilinc-Balci, Molly M. Lamb, Kamonthip Homdayjanakul, Yi Cui, Amy Price, Belinda Heyne, Jaya Sahni, Kareem B. Kabra, Yi-Chan Lin, David Evans, Christopher N. Mores, Ken Page, Larry F. Chu, Eric Haubruge, Etienne Thiry, Louisa F. Ludwig-Begall, Constance Wielick, Tanner Clark, Thor Wagner, Emily Timm, Thomas Gallagher, Peter Faris, Nicolas Macia, Cyrus J. Mackie, Sarah M. Simmons, Susan Reader, Rebecca Malott, Karen Hope, Jan M. Davies, Sarah R. Tritsch, Lorène Dams, Hans Nauwynck, Jean-Francois Willaert, Simon De Jaeger, Lei Liao, Mervin Zhao, Jan Laperre, Olivier Jolois, Sarah J. Smit, Alpa N. Patel, Mark Mayo, Rod Parker, Vanessa Molloy-Simard, Jean-Luc Lemyre, Steven Chu, John M. Conly, May C. Chu
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- Journal:
- Infection Control & Hospital Epidemiology / Volume 43 / Issue 7 / July 2022
- Published online by Cambridge University Press:
- 21 May 2021, pp. 876-885
- Print publication:
- July 2022
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Objective:
The coronavirus disease 2019 (COVID-19) pandemic has resulted in shortages of personal protective equipment (PPE), underscoring the urgent need for simple, efficient, and inexpensive methods to decontaminate masks and respirators exposed to severe acute respiratory coronavirus virus 2 (SARS-CoV-2). We hypothesized that methylene blue (MB) photochemical treatment, which has various clinical applications, could decontaminate PPE contaminated with coronavirus.
Design:The 2 arms of the study included (1) PPE inoculation with coronaviruses followed by MB with light (MBL) decontamination treatment and (2) PPE treatment with MBL for 5 cycles of decontamination to determine maintenance of PPE performance.
Methods:MBL treatment was used to inactivate coronaviruses on 3 N95 filtering facepiece respirator (FFR) and 2 medical mask models. We inoculated FFR and medical mask materials with 3 coronaviruses, including SARS-CoV-2, and we treated them with 10 µM MB and exposed them to 50,000 lux of white light or 12,500 lux of red light for 30 minutes. In parallel, integrity was assessed after 5 cycles of decontamination using multiple US and international test methods, and the process was compared with the FDA-authorized vaporized hydrogen peroxide plus ozone (VHP+O3) decontamination method.
Results:Overall, MBL robustly and consistently inactivated all 3 coronaviruses with 99.8% to >99.9% virus inactivation across all FFRs and medical masks tested. FFR and medical mask integrity was maintained after 5 cycles of MBL treatment, whereas 1 FFR model failed after 5 cycles of VHP+O3.
Conclusions:MBL treatment decontaminated respirators and masks by inactivating 3 tested coronaviruses without compromising integrity through 5 cycles of decontamination. MBL decontamination is effective, is low cost, and does not require specialized equipment, making it applicable in low- to high-resource settings.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. 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- The Cambridge Dictionary of Philosophy
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- Edited by Mark Richardson, Doshisha University, Kyoto
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- Robert Frost in Context
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- 05 April 2014
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Phan, Isabel Apawo Phiri, William S. F. Pickering, Derrick G. Pitard, William Elvis Plata, Zlatko Plese, John Plummer, James Newton Poling, Ronald Popivchak, Andrew Porter, Ute Possekel, James M. Powell, Enos Das Pradhan, Devadasan Premnath, Jaime Adrían Prieto Valladares, Anne Primavesi, Randall Prior, María Alicia Puente Lutteroth, Eduardo Guzmão Quadros, Albert Rabil, Laurent William Ramambason, Apolonio M. Ranche, Vololona Randriamanantena Andriamitandrina, Lawrence R. Rast, Paul L. Redditt, Adele Reinhartz, Rolf Rendtorff, Pål Repstad, James N. Rhodes, John K. Riches, Joerg Rieger, Sharon H. Ringe, Sandra Rios, Tyler Roberts, David M. Robinson, James M. Robinson, Joanne Maguire Robinson, Richard A. H. Robinson, Roy R. Robson, Jack B. Rogers, Maria Roginska, Sidney Rooy, Rev. Garnett Roper, Maria José Fontelas Rosado-Nunes, Andrew C. Ross, Stefan Rossbach, François Rossier, John D. Roth, John K. Roth, Phillip Rothwell, Richard E. Rubenstein, Rosemary Radford Ruether, Markku Ruotsila, John E. Rybolt, Risto Saarinen, John Saillant, Juan Sanchez, Wagner Lopes Sanchez, Hugo N. Santos, Gerhard Sauter, Gloria L. Schaab, Sandra M. Schneiders, Quentin J. Schultze, Fernando F. Segovia, Turid Karlsen Seim, Carsten Selch Jensen, Alan P. F. Sell, Frank C. Senn, Kent Davis Sensenig, Damían Setton, Bal Krishna Sharma, Carolyn J. Sharp, Thomas Sheehan, N. Gerald Shenk, Christian Sheppard, Charles Sherlock, Tabona Shoko, Walter B. Shurden, Marguerite Shuster, B. Mark Sietsema, Batara Sihombing, Neil Silberman, Clodomiro Siller, Samuel Silva-Gotay, Heikki Silvet, John K. Simmons, Hagith Sivan, James C. Skedros, Abraham Smith, Ashley A. Smith, Ted A. Smith, Daud Soesilo, Pia Søltoft, Choan-Seng (C. S.) Song, Kathryn Spink, Bryan Spinks, Eric O. Springsted, Nicolas Standaert, Brian Stanley, Glen H. Stassen, Karel Steenbrink, Stephen J. Stein, Andrea Sterk, Gregory E. Sterling, Columba Stewart, Jacques Stewart, Robert B. Stewart, Cynthia Stokes Brown, Ken Stone, Anne Stott, Elizabeth Stuart, Monya Stubbs, Marjorie Hewitt Suchocki, David Kwang-sun Suh, Scott W. Sunquist, Keith Suter, Douglas Sweeney, Charles H. Talbert, Shawqi N. Talia, Elsa Tamez, Joseph B. Tamney, Jonathan Y. Tan, Yak-Hwee Tan, Kathryn Tanner, Feiya Tao, Elizabeth S. Tapia, Aquiline Tarimo, Claire Taylor, Mark Lewis Taylor, Bishop Abba Samuel Wolde Tekestebirhan, Eugene TeSelle, M. Thomas Thangaraj, David R. Thomas, Andrew Thornley, Scott Thumma, Marcelo Timotheo da Costa, George E. “Tink” Tinker, Ola Tjørhom, Karen Jo Torjesen, Iain R. Torrance, Fernando Torres-Londoño, Archbishop Demetrios [Trakatellis], Marit Trelstad, Christine Trevett, Phyllis Trible, Johannes Tromp, Paul Turner, Robert G. Tuttle, Archbishop Desmond Tutu, Peter Tyler, Anders Tyrberg, Justin Ukpong, Javier Ulloa, Camillus Umoh, Kristi Upson-Saia, Martina Urban, Monica Uribe, Elochukwu Eugene Uzukwu, Richard Vaggione, Gabriel Vahanian, Paul Valliere, T. J. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Contributors
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- By Nalini Vadivelu, Christian J. Whitney, Raymond S. Sinatra, M. Khurram Ghori, Yu-Fan (Robert) Zhang, Raymond S. Sinatra, Joshua Wellington, Yuan-Yi Chia, Francis J. Keefe, Jon McCormack, Ian Power, John Butterworth, P. M. Lavand’homme, M. F. De Kock, Bradley Urie, Oscar A. de Leon-Casasola, Frederick M. Perkins, Larry F. Chu, David Clark, Martin S. Angst, Cynthia M. Welchek, Lisa Mastrangelo, Raymond S. Sinatra, Richard Martinez, Scott S. Reuben, Asokumar Buvanendran, Raymond S. Sinatra, Pamela E Macintyre, Julia Coldrey, Daniel B. Maalouf, Spencer S. Liu, Susan Dabu-Bondoc, Samantha A. Franco, Raymond S. Sinatra, James Benonis, Jennifer Fortney, David Hardman, Gavin Martin, Holly Evans, Karen C. Nielsen, Marcy S. Tucker, Stephen M. Klein, Benjamin Sherman, Ikay Enu, Raymond S. Sinatra, James W. Heitz, Eugene R. Viscusi, Jonathan S. Jahr, Kofi N. Donkor, Raymond S. Sinatra, Manzo Suzuki, Johan Raeder, Vegard Dahl, Stefan Erceg, Keun Sam Chung, Kok-Yuen Ho, Tong J. Gan, Dermot R. Fitzgibbon, Paul Willoughby, Brian E. Harrington, Joseph Marino, Tariq M. Malik, Raymond S. Sinatra, Giorgio Ivani, Valeria Mossetti, Simona Italiano, Thomas M. Halaszynski, Nousheh Saidi, Javier Lopez, Kate Miller, Ferne Braveman, Jaya L. Varadarajan, Steven J. Weisman, Sukanya Mitra, Raymond S. Sinatra, Theodore J. Saclarides, Knox H. Todd, James R. Miner, Chris Pasero, Nancy Eksterowicz, Margo McCaffery, Leslie N. Schechter, Amr E. Abouleish, Govindaraj Ranganathan, Tee Yong Tan, Stephan A. Schug, Marie N. Hanna, Spencer S. Liu, Christopher L. Wu, Craig T. Hartrick, Garen Manvelian, Christine Miaskowski, Brian Durkin, Peter S. A. Glass
- Edited by Raymond S. Sinatra, Oscar A. de Leon-Cassasola, University of Rochester Medical Center, New York, Eugene R. Viscusi, Brian Ginsberg
- Foreword by Henry McQuay
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- Acute Pain Management
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- 26 October 2009
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- 27 April 2009, pp vii-xii
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Random spanning trees of Cayley graphs and an associated compactification of semigroups
- Steven N. Evans
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 42 / Issue 3 / October 1999
- Published online by Cambridge University Press:
- 20 January 2009, pp. 611-620
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A sequential construction of a random spanning tree for the Cayley graph of a finitely generated, countably infinite subsemigroup V of a group G is considered. At stage n, the spanning tree T isapproximated by a finite tree Tn rooted at the identity.The approximation Tn+1 is obtained by connecting edges to the points of V that are not already vertices of Tn but can be obtained from vertices of Tn via multiplication by a random walk step taking values in the generating set of V. This construction leads to a compactification of the semigroup V inwhich a sequence of elements of V that is not eventually constant is convergent if the random geodesic through the spanning tree T that joins the identity to the nth element of the sequence converges in distribution as n→∞. The compactification is identified in a number of examples. Also, it is shown that if h(Tn) and #(Tn) denote, respectively, the height and size of the approximating tree Tn, then there are constants 0<ch≤1 and 0≥c# ≤log2 such that limn→∞ n–1 h(Tn)= ch and limn→∞n–1 log# (Tn)= c# almost surely.
Embedding a Markov Chain into a Random Walk on a Permutation Group
- STEVEN N. EVANS
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- Journal:
- Combinatorics, Probability and Computing / Volume 13 / Issue 3 / May 2004
- Published online by Cambridge University Press:
- 28 April 2004, pp. 339-351
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Using representation theory, we obtain a necessary and sufficient condition for a discrete-time Markov chain on a finite state space $E$ to be representable as $$\Psi_n \Psi_{n-1} \cdots \Psi_1 z,\quad n \geq 0,$$ for any $z \in E$, where the $\Psi_i$ are independent, identically distributed random permutations taking values in some given transitive group of permutations on $E$. The condition is particularly simple when the group is 2-transitive on $E$. We also work out the explicit form of our condition for the dihedral group of symmetries of a regular polygon.
INFINITELY-MANY-SPECIES LOTKA–VOLTERRA EQUATIONS ARISING FROM SYSTEMS OF COALESCING MASSES
- STEVEN N. EVANS
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- Journal:
- Journal of the London Mathematical Society / Volume 60 / Issue 1 / August 1999
- Published online by Cambridge University Press:
- 01 August 1999, pp. 171-186
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- August 1999
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The paper considers nonlinear, probability measure-valued dynamical systems that generalise those classical Lotka–Volterra equations in which, to use ecological terminology, the total size of a finite number of populations of interacting species is conserved. In this generalisation there is a ‘different species’ at each point of an arbitrary measurable space.
Such infinitely-many-species analogues of the classical Lotka–Volterra equations appear as hydrodynamic-type limits of stochastic systems of randomly coalescing masses related to those that have been used to model physical and chemical processes of agglomeration, coagulation and condensation.
One natural instance of this generalisation has closed-form solutions, including a family of solutions that exhibit soliton-like behaviour. The large time asymptotics of other classes of examples can be completely described using analogues of Lyapunov function techniques. Moreover, there are conserved quantities in the form of relative entropies that generalise those found by Volterra in the classical case. Finally, each solution has a series expansion as a time-varying, geometric mixture of a fixed sequence of probability measures. The existence of this expansion is related to the fact that the system is in martingale problem duality with a function-valued Markov process.
Weighted Occupation Time for Branching Particle Systems and a Representation for the Supercritical Superprocess
- Steven N. Evans, Neil O'Connell
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- Journal:
- Canadian Mathematical Bulletin / Volume 37 / Issue 2 / 01 June 1994
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- 20 November 2018, pp. 187-196
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- 01 June 1994
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We obtain a representation for the supercritical Dawson-Watanabe superprocessin terms of a subcritical superprocess with immigration, where the immigration at a given time is governed by the state of an underlying branching particle system. The proof requires a new result on the laws of weighted occupation times for branching particle systems.
Measure-Valued Branching Diffusions with Singular Interactions
- Steven N. Evans, Edwin A. Perkins
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- Journal:
- Canadian Journal of Mathematics / Volume 46 / Issue 1 / 01 February 1994
- Published online by Cambridge University Press:
- 20 November 2018, pp. 120-168
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- 01 February 1994
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The usual super-Brownian motion is a measure-valued process that arises as a high density limit of a system of branching Brownian particles in which the branching mechanism is critical. In this work we consider analogous processes that model the evolution of a system of two such populations in which there is inter-species competition or predation.
We first consider a competition model in which inter-species collisions may result in casualties on both sides. Using a Girsanov approach, we obtain existence and uniqueness of the appropriate martingale problem in one dimension. In two and three dimensions we establish existence only. However, we do show that, in three dimensions, any solution will not be absolutely continuous with respect to the law of two independent super-Brownian motions. Although the supports of two independent super-Brownian motions collide in dimensions four and five, we show that there is no solution to the martingale problem in these cases.
We next study a prédation model in which collisions only affect the "prey" species. Here we can show both existence and uniqueness in one, two and three dimensions. Again, there is no solution in four and five dimensions. As a tool for proving uniqueness, we obtain a representation of martingales for a super-process as stochastic integrals with respect to the related orthogonal martingale measure.
We also obtain existence and uniqueness for a related single population model in one dimension in which particles are killed at a rate proportional to the local density. This model appears as a limit of a rescaled contact process as the range of interaction goes to infinity.
Two representations of a conditioned superprocess
- Steven N. Evans
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 123 / Issue 5 / 1993
- Published online by Cambridge University Press:
- 14 November 2011, pp. 959-971
- Print publication:
- 1993
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We consider a class of measure-valued Markov processes constructed by taking a superprocess over some underlying Markov process and conditioning it to stay alive forever. We obtain two representations of such a process. The first representation is in terms of an “immortal particle” that moves around according to the underlying Markov process and throws off pieces of mass, which then proceed to evolve in the same way that mass evolves for the unconditioned superprocess. As a consequence of this representation, we show that the tail σ-field of the conditioned superprocess is trivial if the tail σ-field of the underlying process is trivial. The second representation is analogous to one obtained by LeGall in the unconditioned case. It represents the conditioned superprocess in terms of a certain process taking values in the path space of the underlying process. This representation is useful for studying the “transience” and “recurrence” properties of the closed support process.
The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction
- Steven N. Evans
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- Journal:
- Canadian Mathematical Bulletin / Volume 35 / Issue 1 / 01 March 1992
- Published online by Cambridge University Press:
- 20 November 2018, pp. 70-74
- Print publication:
- 01 March 1992
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We explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond to starting the conditioned process at the zero measure.
Collision Local Times and Measure-Valued Processes
- Martin T. Barlow, Steven N. Evans, Edwin A. Perkins
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- Journal:
- Canadian Journal of Mathematics / Volume 43 / Issue 5 / 01 October 1991
- Published online by Cambridge University Press:
- 20 November 2018, pp. 897-938
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- 01 October 1991
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We consider two independent Dawson-Watanabe super-Brownian motions, Y1 and Y2. These processes are diffusions taking values in the space of finite measures on ℝd. We show that if d ≤ 5 then with positive probability there exist times t such that the closed supports of intersect; whereas if d > 5 then no such intersections occur. For the case d ≤ 5, we construct a continuous, non-decreasing measure–valued process L(Y1, Y2), the collision local time, such that the measure defined by , is concentrated on the set of times and places at which intersections occur. We give a Tanaka-like semimartingale decomposition of L(Y1, Y2). We also extend these results to a certain class of coupled measurevalued processes. This extension will be important in a forthcoming paper where we use the tools developed here to construct coupled pairs of measure-valued diffusions with point interactions. In the course of our proofs we obtain smoothness results for the random measures that are uniform in t. These theorems use a nonstandard description of Yi and are of independent interest.
Perturbation of functions by the paths of a Lévy process
- Steven N. Evans
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- Journal:
- Mathematical Proceedings of the Cambridge Philosophical Society / Volume 105 / Issue 2 / March 1989
- Published online by Cambridge University Press:
- 24 October 2008, pp. 377-380
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- March 1989
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In a recent paper Mountford [4] showed, using an ingenious probabilistic argument, that if X is a real-valued stable process with index α < 1 and f: [0, ∞) → ℝ is a non-constant continuous function, then
where we use the notation |A| for the Lebesgue measure of a Lebesgue measurable set A ⊂ ℝ. The argument in [4] appears to make strong use of the strict scaling properties of X and the ‘intermediate value’ property of f.
The maximum distribution of a Gaussian stochastic process indexed by a local field
- Part of
- Steven N. Evans
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 46 / Issue 1 / February 1989
- Published online by Cambridge University Press:
- 09 April 2009, pp. 69-87
- Print publication:
- February 1989
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We consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.
On the Hausdorff dimension of Brownian cone points
- Steven N. Evans
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- Journal:
- Mathematical Proceedings of the Cambridge Philosophical Society / Volume 98 / Issue 2 / September 1985
- Published online by Cambridge University Press:
- 24 October 2008, pp. 343-353
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- September 1985
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Let B(t) be a two-dimensional Brownian motion. For 0 < α < 2π, set
and, for 0 ≥ β< 2π, let F(α,β) be F(α) rotated through an angle β about the origin.