Stochastic Partial Differential Equations

doi:10.1017/CBO9780511526213

Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on stochastic partial differential equations. Subjects covered include the stochastic Navier–Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations this book will have much to offer.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Foreword
pp vii-viii
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List of participants
pp ix-x
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Stochastic differential equations with boundary conditions and the change of measure method
pp 1-21
- By Aureli Alabert, Universitat Autònoma de Barcelona, Departament de Matemàtiques. 08193-Bellaterra, Catalonia.
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The Martin boundary of the Brownian sheet
pp 22-30
- By Oliver Brockhaus, Institut für Angewandte Mathematik, Universität Bonn
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Neocompact sets and stochastic Navier-Stokes equations
pp 31-54
- By Nigel J. Cutland, School of Mathematics, University of Hull. Hull HU6 7RX, UK., H. Jerome Keisler, Department of Mathematics, University of Wisconsin. Madison, WI 537506, USA.
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Numerical experiments with S(P)DE's
pp 55-71
- By J. G. Gaines, Dept. of Mathematics and Statistics, University of Edinburgh, JCMB, Kings Buildings, Mayfield Rd. Edinburgh EH9 3JZ, UK
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Contour processes of random trees
pp 72-96
- By J. Geiger, Department of Mathematics, Frankfurt University. D-60054 Frankfurt, Germany.
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On a class of quasilinear stochastic differential equations of parabolic type: regular dependence of solutions on initial data
pp 97-119
- By N. Yu. Goncharuk, Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. and Kiev Polytechnical Institute, Department of Mathematical Methods in System Analysis, 37 Pobedy Pr., 252056 Kiev, Ukraine
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Fluctuations of a two-level critical branching system
pp 120-125
- By Luis G. Gorostiza, Departamento de Matemáticas, Centro de Investigatión y de Estudios Avanzados, México
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Non-persistence of two-level branching particle systems in low dimensions
pp 126-140
- By Kenneth J. Hochberg, Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, Anton Wakolbinger, Fachbereich Mathematik, J.W. Goethe-Universitat, D-60054 Frankfurt am Main, Germany, wakolbinOmath.uni-frankfurt.de
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The stochastic Wick-type Burgers equation
pp 141-161
- By H. Holden, Dept. of Mathematical Sciences, Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim, Norway, T. Lindstrøm, Dept. of Mathematics, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway, B. Øksendal, Dept. of Mathematics/VISTA, University of Oslo, Box 1053, Blindern, N-0316 Oslo, Norway, J. Ubøe, Dept. of Mathematics, National College of Safety Engineering, Skåregt. 103, N-5500 Haugesund, Norway., T. -S. Zhang, Dept. of Mathematics, National College of Safety Engineering, Skåregt. 103, N-5500 Haugesund, Norway.
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A weak interaction epidemic among diffusing particles
pp 162-180
- By Ingemar Kaj, Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden
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Noise and dynamic transitions
pp 181-188
- By G. D. Lythe, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK
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Backward stochastic differential equations and quasilinear partial differential equations
pp 189-208
- By Xuerong Mao, Department of Statistics and Modelling Science, University of Strathclyde, Glasgow Gl 1XH, Scotland, U.K.
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Path integrals and finite dimensional filters
pp 209-229
- By S. J. Maybank, Robotics Research Laboratory, University of Oxford. Department of Engineering Science, 19 Parks Road, Oxford OX1 3PJ, UK.
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A skew-product representation for the generator of a two sex population model
pp 230-240
- By Joachim A. Rebholz, Department of Mathematics, University of California at Berkeley, Berkeley, Ca 94720
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A nonlinear hyperbolic SPDE: approximations and support
pp 241-261
- By Carles Rovira, Facultat de Màtematiques, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona-Spain, Marta Sanz-Solé, Facultat de Màtematiques, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona-Spain
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Statistical dynamics with thermal noise
pp 262-286
- By R. F. Streater, King's College, Strand, London WC2R 2LS
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Stochastic Hamilton-Jacobi equations
pp 287-303
- By A. Truman, Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K., H. Z. Zhao, Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.
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On backward filtering equations for SDE systems (direct approach)
pp 304-311
- By A. Yu Veretennikov, Institute for Information Transmission Sciences, Russian Academy of Sciences, 19 Ermolovoy str., 101447, Moscow, Russia
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Ergodicity of Markov semigroups
pp 312-337
- By Boguslaw Zegarlinski, Department of Mathematics, Imperial College, London, UK
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Stochastic Partial Differential Equations

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Foreword
pp vii-viii

List of participants
pp ix-x

Stochastic differential equations with boundary conditions and the change of measure method
pp 1-21

The Martin boundary of the Brownian sheet
pp 22-30

Neocompact sets and stochastic Navier-Stokes equations
pp 31-54

Numerical experiments with S(P)DE's
pp 55-71

Contour processes of random trees
pp 72-96

On a class of quasilinear stochastic differential equations of parabolic type: regular dependence of solutions on initial data
pp 97-119

Fluctuations of a two-level critical branching system
pp 120-125

Non-persistence of two-level branching particle systems in low dimensions
pp 126-140

The stochastic Wick-type Burgers equation
pp 141-161

A weak interaction epidemic among diffusing particles
pp 162-180

Noise and dynamic transitions
pp 181-188

Backward stochastic differential equations and quasilinear partial differential equations
pp 189-208

Path integrals and finite dimensional filters
pp 209-229

A skew-product representation for the generator of a two sex population model
pp 230-240

A nonlinear hyperbolic SPDE: approximations and support
pp 241-261

Statistical dynamics with thermal noise
pp 262-286

Stochastic Hamilton-Jacobi equations
pp 287-303

On backward filtering equations for SDE systems (direct approach)
pp 304-311

Ergodicity of Markov semigroups
pp 312-337

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