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    Molchanov, Ilya 2017. Theory of Random Sets. Vol. 87, Issue. , p. 1.

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    Molchanov, Ilya 2017. Theory of Random Sets. Vol. 87, Issue. , p. 451.

    Last, Günter and Ziesche, Sebastian 2017. On the Ornstein–Zernike equation for stationary cluster processes and the random connection model. Advances in Applied Probability, Vol. 49, Issue. 04, p. 1260.

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    Lectures on the Poisson Process
    • Online ISBN: 9781316104477
    • Book DOI: https://doi.org/10.1017/9781316104477
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Book description

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

Reviews

'An understanding of the remarkable properties of the Poisson process is essential for anyone interested in the mathematical theory of probability or in its many fields of application. This book is a lucid and thorough account, rigorous but not pedantic, and accessible to any reader familiar with modern mathematics at first degree level. Its publication is most welcome.'

J. F. C. Kingman - University of Bristol

'I have always considered the Poisson process to be a cornerstone of applied probability. This excellent book demonstrates that it is a whole world in and of itself. The text is exciting and indispensable to anyone who works in this field.'

Dietrich Stoyan - Technische Universität Bergakademie Freiberg , Germany

'Last and Penrose’s Lectures on the Poisson Process constitutes a splendid addition to the monograph literature on point processes. While emphasizing the Poisson and related processes, their mathematical approach also covers the basic theory of random measures and various applications, especially to stochastic geometry. They assume a sound grounding in measure-theoretic probability, which is well summarized in two appendices (on measure and probability theory). Abundant exercises conclude each of the twenty-two ‘lectures’ which include examples illustrating their ‘course’ material. It is a first-class complement to John Kingman’s essay on the Poisson process.'

Daryl Daley - University of Melbourne

'Pick n points uniformly and independently in a cube of volume n in Euclidean space. The limit of these random configurations as n → ∞ is the Poisson process. This book, written by two of the foremost experts on point processes, gives a masterful overview of the Poisson process and some of its relatives. Classical tenets of the Theory, like thinning properties and Campbell’s formula, are followed by modern developments, such as Liggett’s extra heads theorem, Fock space, permanental processes and the Boolean model. Numerous exercises throughout the book challenge readers and bring them to the edge of current theory.'

Yuval Peres - Microsoft Research and National Academy of Sciences

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References
[1] Abbe, E. (1895). Berechnung des wahrscheinlichen Fehlers bei der Bestimmung von Mittelwerthen durch Abzählen. In: Hensen, V. Methodik der Untersuchungen bei der Plankton-Expedition der Humboldt-Stiftung. Verlag von Lipsius & Tischer, Kiel, pp. 166–169.
[2] Adler, R. and Taylor J., E. (2007). Random Fields and Geometry. Springer, New York.
[3] Aldous, D. (1988). Probability Approximations via the Poisson Clumping Heuristic. Springer, New York.
[4] Baccelli, F. and Błaszczyszyn, B. (2009). Stochastic Geometry andWireless Networks, Volume I - Theory. NoW Publishers, Boston.
[5] Baccelli, F. and Błaszczyszyn, B. (2009). Stochastic Geometry andWireless Networks, Volume II - Applications. NoW Publishers, Boston.
[6] Baccelli, F. and Brémaud, P. (2000). Elements of Queueing Theory. Springer, Berlin.
[7] Baddeley, A. (1980). A limit theorem for statistics of spatial data. Adv. in Appl. Probab. 12, 461–.
[8] Baddeley, A., Rubak, E. and Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R. Chapman & Hall and CRC Press, London.
[9] Bateman, H. (1910). Note on the probability distribution of α-particles. Philos. Mag. 20 (6), 704–707.
[10] Bertoin, J. (1996). Lévy Processes. Cambridge University Press, Cambridge.
[11] Bhabha, H.J. (1950). On the stochastic theory of continuous parametric systems and its application to electron cascades. Proc. R. Soc. London Ser. A 202, 301–322.
[12] Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.
[13] Billingsley, P. (1995). Probability and Measure. 3rd edn. Wiley, New York.
[14] Błaszczyszyn, B. (1995). Factorial moment expansion for stochastic systems. Stoch. Proc. Appl. 56, 335–.
[15] Błaszczyszyn, B., Merzbach, E. and Schmidt, V. (1997). A note on expansion for functionals of spatial marked point processes. Statist. Probab. Lett. 36, 306–.
[16] Bogachev, V.I. (2007). Measure Theory. Springer, Berlin.
[17] Bortkiewicz, L. von (1898). Das Gesetz der kleinen Zahlen. BG Teubner, Leipzig.
[18] Brémaud, P. (1981). Point Processes and Queues. Springer, New York.
[19] Campbell, N. (1909). The study of discontinuous phenomena. Proc. Cambridge Philos. Soc. 15, 136–.
[20] Chatterjee, S. (2008). A new method of normal approximation. Ann. Probab. 36, 1610–.
[21] Chatterjee, S. (2009). Fluctuations of eigenvalues and second order Poincaré inequalities. Probab. Theory Related Fields 143, 40–.
[22] Chen, L. (1985). Poincaré-type inequalities via stochastic integrals. Z. Wahrsch. verw. Gebiete 69, 277–.
[23] Chiu, S.N., Stoyan, D., Kendall,W.S. and Mecke, J. (2013). Stochastic Geometry and its Applications. 3rd edn. Wiley, Chichester.
[24] Copeland, A.H. and Regan, F. (1936). A postulational treatment of the Poisson law. Ann. of Math. 37, 362–.
[25] Cox, D.R. (1955). Some statistical methods connected with series of events. J. R. Statist. Soc. Ser. B 17, 164–.
[26] Cramér, H. (1969). Historical review of Filip Lundberg's works on risk theory. Scand. Actuar. J. (suppl. 3), 6–12.
[27] Daley, D.J. and Vere-Jones, D. (2003/2008). An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods, Volume II: General Theory and Structure. 2nd edn. Springer, New York.
[28] Davy, P. (1976). Projected thick sections through multi-dimensional particle aggregates. J. Appl. Probab. 13, 722–. Correction: J. Appl. Probab. 15 (1978), 456.
[29] Doob, J.L. (1953). Stochastic Processes. Wiley, New York.
[30] Dudley, R.M. (2002). Real Analysis and Probability. Cambridge University Press, Cambridge.
[31] Dwass, M. (1964). Extremal processes. Ann. Math. Statist. 35, 1725–.
[32] Ellis, R.L. (1844). On a question in the theory of probabilities. Cambridge Math. J. 4, 127–133. [Reprinted in W. Walton (ed.) (1863). The Mathematical and Other Writings of Robert Leslie Ellis. Deighton Bell, Cambridge, pp. 173–179.]
[33] Erlang, A.K. (1909). The theory of probabilities and telephone conversations. Nyt. Tidsskr. f. Mat. B 20, 39–.
[34] Esary, J.D. and Proschan, F. (1963). Coherent structures of non-identical components. Technometrics 5, 209–.
[35] Federer, H. (1969). Geometric Measure Theory. Springer, New York.
[36] Feller, W. (1940). On the time distribution of so-called random events. Phys. Rev. 57, 908–.
[37] Ferguson, T.S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 230–.
[38] Fichtner, K.H. (1975). Charakterisierung Poissonscher zufälliger Punktfolgen und infinitesemale Verdünnungsschemata. Math. Nachr. 68, 104–.
[39] Finetti, B. de (1929). Sulle funzioni a incremento aleatorio. Rend. Acc. Naz. Lincei 10, 168–.
[40] Franceschetti, M., Penrose, M.D. and Rosoman, T. (2011). Strict inequalities of critical values in continuum percolation. J. Stat. Phys. 142, 486–.
[41] Gale, D. and Shapley, L.S. (1962). College admissions and the stability of marriage. Amer. Math. Monthly 69, 14–.
[42] Gilbert, E.N. (1961). Random plane networks. J. Soc. Indust. Appl. Math. 9, 543–.
[43] Grandell, J. (1976). Doubly Stochastic Poisson Processes. Lect. Notes in Math. 529, Springer, Berlin.
[44] Guttorp, P. and Thorarinsdottir, T.L. (2012). What happened to discrete chaos, the Quenouille process, and the sharp Markov property? Some history of stochastic point processes. Int. Stat. Rev. 80, 268–.
[45] Hall, P. (1988). Introduction to the Theory of Coverage Processes. Wiley, New York.
[46] Harris, T.E. (1960). A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56, 20–.
[47] Heinrich, L. and Molchanov, I. (1999). Central limit theorem for a class of random measures associated with germ–grain models. Adv. in Appl. Probab. 31, 314–.
[48] Hoffman, C., Holroyd, A.E. and Peres, Y. (2006). A stable marriage of Poisson and Lebesgue. Ann. Probab. 34, 1272–.
[49] Holroyd, A.E. and Peres, Y. (2005). Extra heads and invariant allocations. Ann. Probab. 33, 52–.
[50] Houdré, C. and Privault, N. (2002). Concentration and deviation inequalities in infinite dimensions via covariance representations. Bernoulli 8, 720–.
[51] Hough, J.B., Krishnapur, M., Peres, Y. and Viág, B. (2006). Determinantal processes and independence. Probab. Surv. 3, 229–.
[52] Hug, D., Last, G. and Schulte, M. (2016). Second order properties and central limit theorems for geometric functionals of Boolean models. Ann. Appl. Probab. 26, 135–.
[53] Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, Chichester.
[54] Itô, K. (1941). On stochastic processes (I). Jpn. J. Math. 18, 301–.
[55] Itô, K. (1951). Multiple Wiener integral. J. Math. Soc. Japan 3, 169–.
[56] Itô, K. (1956). Spectral type of the shift transformation of differential processes with stationary increments. Trans. Amer. Math. Soc. 81, 263–.
[57] Ito, Y. (1988). Generalized Poisson functionals. Probab. Theory Related Fields 77, 28–.
[58] Janossy, L. (1950). On the absorption of a nucleon cascade. Proc. R. Irish Acad. Sci. Sec. A 53, 188–.
[59] Jörgens, K. (1982). Linear Integral Operators. Pitman, Boston.
[60] Kabanov, Y.M. (1975). On extended stochastic integrals. Theory Probab. Appl. 20, 722–.
[61] Kallenberg, O. (1973). Characterization and convergence of random measures and point processes. Z. Wahrsch. verw. Gebiete 27, 21–.
[62] Kallenberg, O. (1986). Random Measures. 4th edn. Akademie-Verlag and Academic Press, Berlin and London.
[63] Kallenberg, O. (2002). Foundations of Modern Probability. 2nd edn. Springer, New York.
[64] Kallenberg, O. (2011). Invariant Palm and related disintegrations via skew factorization. Probab. Theory Related Fields 149, 301–.
[65] Kallenberg, O. (2017). Random Measures, Theory and Applications. Springer, Cham.
[66] Kallenberg, O. and Szulga, J. (1989). Multiple integration with respect to Poisson and Lévy processes. Probab. Theory Related Fields 83, 134–.
[67] Keane, M.S. (1991). Ergodic theory and subshifts of finite type. In: Bedford, T., Keane M. and Series, C. (eds.) Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces. Oxford University Press, Oxford.
[68] Kerstan, J., and Matthes, K. (1964). Stationäre zufällige Punktfolgen II. Jahresber. Deutsch. Math. Ver. 66, 118–.
[69] Kerstan, J., Matthes, K. and Mecke, J. (1974). Unbegrenzt Teilbare Punktprozesse. Akademie-Verlag, Berlin.
[70] Khinchin, A.Y. (1933). Asymptotische Gesetze der Wahrscheinlichkeitsrechnung. Springer, Berlin.
[71] Khinchin, A.Y. (1937). A new derivation of one formula by P. Lévy. Bull. Moscow State Univ. 1, 5–.
[72] Khinchin, A.Y. (1955). Mathematical Methods in the Theory of Queuing (in Russian). Trudy Mat. Inst. Steklov 49. English transl. (1960): Griffin, London.
[73] Khinchin, A.Y. (1956). Sequences of chance events without after-effects. Theory Probab. Appl. 1, 15–.
[74] Kingman, J.F.C. (1967). Completely random measures. Pacific J. Math. 21, 59–78.
[75] Kingman, J.F.C. (1993). Poisson Processes. Oxford University Press, Oxford.
[76] Kingman, J.F.C. (2006). Poisson processes revisited. Probab. Math. Statist. 26, 95–.
[77] Kolmogorov, A.N. (1932). Sulla forma generale di un processo stocastico omogeneo. Atti Accad. Naz. Lincei 15, 808–.
[78] Krantz, S. and Parks, H.R. (2002). A Primer of Real Analytic Functions. Birkhäuser, Boston.
[79] Krickeberg, K. (1972). The Cox process. Sympos. Math. 9, 167–.
[80] Krickeberg, K. (1974). Moments of point processes. In: Harding, E.F. and Kendall, D.G. (eds.) Stochastic Geometry. Wiley, London, pp. 89–113.
[81] Krickeberg, K. (1982). Processus ponctuels en statistique. In: Hennequin, P. (ed.) École d'été de probabilités de Saint-Flour X - 1980. Lect. Notes in Math. 929, Springer, Berlin, pp. 205–313.
[82] Krickeberg, K. (2014). Point Processes: A Random Radon Measure Approach. Walter Warmuth Verlag, Berlin. (Augmented with several Scholia by Hans Zessin.)
[83] Kyprianou, A. (2006). Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin.
[84] Last, G. (2006). Stationary partitions and Palm probabilities. Adv. in Appl. Probab. 37, 620–.
[85] Last, G. (2010). Modern random measures: Palm theory and related models. In: Kendall, W. and Molchanov, I. (eds.) New Perspectives in Stochastic Geometry. Oxford University Press, Oxford, pp. 77-110.
[86] Last, G. (2014). Perturbation analysis of Poisson processes. Bernoulli 20, 486–513.
[87] Last, G. (2016). Stochastic analysis for Poisson processes. In: Peccati, G. and Reitzner, M. (eds.) Stochastic Analysis for Poisson Point Processes. Springer, Milan, pp. 1–36.
[88] Last, G. and Brandt, A. (1995). Marked Point Processes on the Real Line: The Dynamic Approach. Springer, New York.
[89] Last, G., Peccati, G. and Schulte, M. (2016). Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization. Probab. Theory Related Fields 165, 723–.
[90] Last, G. and Penrose, M.D. (2011). Poisson process Fock space representation, chaos expansion and covariance inequalities. Probab. Theory Related Fields 150, 690–.
[91] Last, G. and Penrose, M.D. (2011). Martingale representation for Poisson processes with applications to minimal variance hedging. Stoch. Proc. Appl. 121, 1606–.
[92] Last, G., Penrose, M.D., Schulte, M. and Thäle, C. (2014). Moments and central limit theorems for some multivariate Poisson functionals. Adv. in Appl. Probab. 46, 364–.
[93] Last, G. and Thorisson, H. (2009). Invariant transports of stationary random measures and mass-stationarity. Ann. Probab. 37, 813–.
[94] Lee, P.M. (1967). Infinitely divisible stochastic processes. Z. Wahrsch. verw. Gebiete 7, 160–.
[95] Lévy, P. (1934). Sur les intégrales dont les éléments sont des variables aléatoires indépendantes. Ann. Scuola Norm. Sup. Pisa (Ser. II) 3, 366–
[96] Liggett, T.M. (2002). Tagged particle distributions or how to choose a head at random. In: Sidoravicious, V. (ed.) In and Out of Equlibrium. Birkhäuser, Boston, pp. 133-162.
[97] Lundberg, F. (1903). I. Approximerad Framställning av Sannolikhetsfunktionen. II. Återförsäkring av Kollektivrisker. Akad. Afhandling, Almqvist & Wiksell, Uppsala.
[98] Macchi, O. (1971). Distribution statistique des instants d'émission des photo- électrons d'une lumi`ere thermique. C.R. Acad. Sci. Paris Ser. A 272, 440–.
[99] Macchi, O. (1975). The coincidence approach to stochastic point processes. Adv. in Appl. Probab. 7, 122–.
[100] Margulis, G. (1974). Probabilistic characteristics of graphs with large connectivity. Problemy Peredachi Informatsii 10, 108–.
[101] Matheron, G. (1975). Random Sets and Integral Geometry. Wiley, New York.
[102] Matthes, K. (1964). Stationäre zufällige Punktfolgen I. Jahresber. Dtsch. Math.- Ver. 66, 79–.
[103] Matthes, K., Kerstan, J. and Mecke, J. (1978). Infinitely Divisible Point Processes. Wiley, Chichester (English edn. of [69]).
[104] McCullagh, P. and Møller, J. (2006). The permanental process. Adv. in Appl. Probab. 38, 888–.
[105] Mecke, J. (1967). Stationäre zufällige Maße auf lokalkompakten Abelschen Gruppen. Z. Wahrsch. verw. Geb. 9, 58–.
[106] Mecke, J. (2011). Random Measures: Classical Lectures. Walter Warmuth Verlag.
[107] Meester, R. and Roy, R. (1996). Continuum Percolation. Cambridge University Press, Cambridge.
[108] Miles, R.E. (1976). Estimating aggregate and overall characteristics from thick sections by transmission microscopy. J. Microsc. 107, 233–.
[109] Møller, J. (2003). Shot noise Cox processes. Adv. in Appl. Probab. 35, 640–.
[110] Mönch, G. (1971). Verallgemeinerung eines Satzes von A. Rényi. Studia Sci. Math. Hung. 6, 90–.
[111] Moivre, A. de (1711). On the measurement of chance, or, on the probability of events in games depending upon fortuitous chance. Phil. Trans. 329 (Jan.-Mar.) English transl. (1984): Int. Stat. Rev. 52, 262–.
[112] Molchanov, I. (1995). Statistics of the Boolean model: from the estimation of means to the estimation of distributions. Adv. in Appl. Probab. 27, 86–.
[113] Molchanov, I. (2005). Theory of Random Sets. Springer, London.
[114] Molchanov, I. and Zuyev, S. (2000). Variational analysis of functionals of Poisson processes. Math. Operat. Res. 25, 508–.
[115] Moran, P.A.P. (1952). A characteristic property of the Poisson distribution. Proc. Cambridge Philos. Soc. 48, 207–.
[116] Moyal, J.E. (1962). The general theory of stochastic population processes. Acta Math. 108, 31–.
[117] Nehring, B. (2014). A characterization of the Poisson process revisited. Electron. Commun. Probab. 19, 5–.
[118] Newcomb, S. (1860). Notes on the theory of probabilities. The Mathematical Monthly 2, 140–.
[119] Nguyen, X.X. and Zessin, H. (1979). Ergodic theorems for spatial processes. Z. Wahrsch. verw. Geb. 48, 158–.
[120] Nieuwenhuis, G. (1994). Bridging the gap between a stationary point process and its Palm distribution. Stat. Neerl. 48, 62–.
[121] Nourdin, I. and Peccati, G. (2012). Normal Approximations with Malliavin Calculus: From Stein's Method to Universality. Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge.
[122] Palm, C. (1943). Intensity variations in telephone traffic. Ericsson Technics 44, 189–. English transl. (1988): North-Holland, Amsterdam.
[123] Peccati, G. and Reitzner, M. (eds.) (2016). Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener–Itô Chaos Expansions and Stochastic Geometry. Bocconi & Springer Series 7. Springer.
[124] Peccati, G., Solé, J.L., Taqqu, M.S. and Utzet, F. (2010). Stein's method and normal approximation of Poisson functionals. Ann. Probab. 38, 478–.
[125] Peccati, G. and Taqqu, M. (2011). Wiener Chaos: Moments, Cumulants and Diagrams: A Survey with Computer Implementation. Springer, Milan.
[126] Penrose, M. (2003). Random Geometric Graphs. Oxford University Press, Oxford.
[127] Penrose, M.D. (2001). A central limit theorem with applications to percolation, epidemics and Boolean models. Ann. Probab. 29, 1546–.
[128] Penrose, M.D. (2007). Gaussian limits for random geometric measures. Electron. J. Probab. 12 (35), 989–1035.
[129] Penrose, M.D. and Wade, A.R. (2008). Multivariate normal approximation in geometric probability. J. Stat. Theory Pract. 2, 326–.
[130] Penrose, M.D. and Yukich, J.E. (2001). Central limit theorems for some graphs in computational geometry. Ann. Appl. Probab. 11, 1041–.
[131] Penrose, M.D. and Yukich, J.E. (2005). Normal approximation in geometric probability. In: Barbour, A.D. and Chen, L.H.Y. (eds.) Stein's Method and Applications. World Scientific, Singapore, pp. 37–58.
[132] Poisson, S.D. (1837). Recherches sur la Probabilité des Judgements en Mati`ere Criminelle et en Mati`ere Civile, Précédées des R`egles Générales du Calcul des Probabilités. Bachelier, Paris.
[133] Prékopa, A. (1958). On secondary processes generated by a random point distribution of Poisson type. Annales Univ. Sci. Budapest de Eotvos Nom. Sectio Math. 1, 170–.
[134] Reiss, R.-D. (1993). A Course on Point Processes. Springer, New York.
[135] Reitzner, M. and Schulte, M. (2012). Central limit theorems for U-statistics of Poisson point processes. Ann. Probab. 41, 3909–.
[136] Rényi, A. (1956). A characterization of Poisson processes. Magyar Tud. Akad. Mat. Kutató Int. Közl 1, 527–.
[137] Rényi, A. (1962). Théorie des éléments saillants d'une suite d'observations. Annales scientifiques de l'Université de Clermont 2, tome 8, Mathématiques 2, 7–13.
[138] Rényi, A. (1967). Remarks on the Poisson process. Studia Sci. Math. Hung. 2, 123–.
[139] Resnick, S.I. (1987). Extreme Values, Regular Variation and Point Processes. Springer, New York.
[140] Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion. Springer, Berlin.
[141] Roy, R. (1990). The Russo–Seymour–Welsh theorem and the equality of critical densities and the “dual” critical densities for continuum percolation on R2. Ann. Probab. 18, 1575–.
[142] Russo, L. (1981). On the critical percolation probabilities. Z. Wahrsch. verw. Geb. 56, 237–.
[143] Ryll-Nardzewski, C. (1953). On the non-homogeneous Poisson process (I). Studia Math. 14, 128–.
[144] Ryll-Nardzewski, C. (1954). Remarks on the Poisson stochastic process (III). (On a property of the homogeneous Poisson process.) Studia Math. 14, 314–318.
[145] Ryll-Nardzewski, C. (1961). Remarks on processes of calls. Proc. 4th Berkeley Symp. on Math. Statist. Probab. 2, 465–.
[146] Schneider, R. (2013). Convex Bodies: The Brunn–Minkowski Theory. 2nd (expanded) edn. Cambridge University Press, Cambridge.
[147] Schneider, R. and Weil, W. (2008). Stochastic and Integral Geometry. Springer, Berlin.
[148] Seneta, E. (1983). Modern probabilistic concepts in the work of E. Abbe and A. de Moivre. Math. Sci. 8, 80–.
[149] Serfozo, R. (1999). Introduction to Stochastic Networks. Springer, New York.
[150] Shirai, T. and Takahashi, Y. (2003). Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes. J. Funct. Anal. 205, 463–.
[151] Slivnyak, I.M. (1962). Some properties of stationary flows of homogeneous random events. Theory Probab. Appl. 7, 341–.
[152] Srinivasan, S.K. (1969). Stochastic Theory and Cascade Processes. American Elsevier, New York.
[153] Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In: Le Cam, L. Neyman, J. and Scott, E.L. (eds.) Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2: Probability Theory. University of Berkeley Press, Berkeley, pp. 583–602.
[154] Surgailis, D. (1984). On multiple Poisson stochastic integrals and associated Markov semigroups. Probab. Math. Statist. 3, 239–.
[155] Teichmann, J., Ballani, F. and Boogaart, K.G. van den (2013). Generalizations of Matérn's hard-core point processes. Spat. Stat. 9, 53–.
[156] Thorisson, H. (1996). Transforming random elements and shifting random fields. Ann. Probab. 24, 2064–.
[157] Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer, New York.
[158] Vere-Jones, D. (1997). Alpha permanents and their applications to multivariate Gamma, negative binomial and ordinary binomial distributions. New Zealand J. Math. 26, 149–.
[159] Wiener, N. (1938). The homogeneous chaos. Amer. J. Math. 60, 936–.
[160] Wiener, N. and Wintner, A. (1943). The discrete chaos. Amer. J. Math. 65, 279–298.
[161] Wu, L. (2000). A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields 118, 438–.
[162] Zessin, H. (1983). The method of moments for random measures. Z. Wahrsch. verw. Geb. 83, 409–.
[163] Zuyev, S.A. (1992). Russo's formula for Poisson point fields and its applications. Diskretnaya Matematika 4, 149–160 (in Russian). English transl. (1993): Discrete Math. Appl. 3, 73–.

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