Handbook of Statistics 19: Stochastic Processes: Theory and Methods

Edited by

  • D.N. Shanbhag, c/o Probability and Statistics Section, School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
  • C.R. Rao, Statistics Department, 326 Classroom Bldg. University Park, PA 16802-2111, USA

J. Neyman, one of the pioneers in laying the foundations of modern statistical theory, stressed the importance of stochastic processes in a paper written in 1960 in the following terms: "Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research, if treated realistically, does not involve operations on stochastic processes". Arising from the need to solve practical problems, several major advances have taken place in the theory of stochastic processes and their applications. Books by Doob (1953; J. Wiley and Sons), Feller (1957, 1966; J. Wiley and Sons) and Loève (1960; D. van Nostrand and Col., Inc.) among others, have created growing awareness and interest in the use of stochastic processes in scientific and technological studies.
The literature on stochastic processes is very extensive and is distributed in several books and journals. There is a need to review the different lines of researches and developments in stochastic processes and present a consolidated and comprehensive account for the benefit of students, research workers, teachers and consultants. With this in view, North Holland has decided to bring out two volumes in the series, Handbook of Statistics with the titles: Stochastic Processes: Theory and Methods and Stochastic Processes: Modeling and Simulation. The second volume, which is under preparation will be published soon, too.
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Book information

  • Published: January 2001
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-50014-4


A huge number of definitions, properties expressed in the theorem form, and applications of stochastic processes, formulated in formalized but precise mathematical formula language, make this book very useful for those not specialized in the theory of stochastic processes. Statisticians will especially benefit from this book as it shows new areas in which statistics can be applied.
W. Szymczak, Int. Jnl of Occupational Medicine and Environmental Health, Vol. 15 no. 1, 2002

Table of Contents

Preface. Contributors.
1. Pareto Processes (Barry C. Arnold).
2. Branching Processes (K.B. Athreya, A.N. Vidyashankar).
3. Inference in Stochastic Processes (I.V. Basawa).
4. Topics in Poisson Approximation (A.D. Barbour).
5. Some Elements on Lévy Processes (Jean Bertoin).
6. Iterated Random Maps and Some Classes of Markov Processes (Rabi Bhattacharya, Edward C. Waymire).
7. Random Walk and Fluctuation Theory (N.H. Bingham).
8. A Semigroup Representation and Asymptotic Behavour of Certain Statistics of the Fisher-Wright-Moran Coalescent (Adam Bobrowski, Marek Kimmel, Ovide Arino, Ranajit Chakraborty).
9. Continuous-Time ARMA Processes (P.J. Brockwell).
10 .Record Sequences and their Applications (John Bunge, Charles M. Goldie).
11.Stochastic Networks with Product Form Equilibrium (Hans Daduna).
12. Stochastic Processes in Insurance and Finance (Paul Embrechts, Rüdiger Frey, Hansjörg Furror).
13. Renewal Theory (D.R. Grey).
14. The Kolmogorov Isomorphism Theorem and Extensions to some Nonstationary Processes (Yûichirô Kakihara).
15. Stochastic Processes in Reliability (Masaaki Kijima, Haijun Laijun, Moshe Shaked).
16. On the supports of Stochastic Processes of Multiplicity One (A. Klopotowski, M.G. Nadkarni).
17. Gaussian Processes: Inequalities, Small Ball Probabilities and Applications (W.V. Li, Qi-M. Shao).
18. Point Processes and Some Related Processes (Robin K. Milne).
19. Characterization and Identifiability for Stochastic Processes (B.L.S. Prakasa Rao).
20. Associated Sequences and Related Inference Problems (B.L.S. Prakasa Rao, Isha Dewan).
21. Exchangeability, Functional Equations, and Characterizations (C.R. Rao, D.N. Shanbhag).
22. Martingales and Some Applications (M.M. Rao).
23. Markov Chains: Structure and Applications (R.L. Tweedie).
24. Diffusion Processes (S.R.S. Varadhan).
25. Itô's Stochastic Calculus and Its Applications (S. Watanabe).