Handbook of statistics 19: Stochastic processes, theory and methods

C.R. Rao0444500146, 9780444500144

Hardbound. 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.

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Table of contents :
Handbook of statistics 19: Stochastic processes, theory and methods……Page 1
Table of contents……Page 3
Preface……Page 11
Contributors……Page 13
1. Pareto Processes……Page 16
2. Branching Processes……Page 49
3. Inference in Stochastic Processes……Page 68
4. Topics in Poisson Approximation……Page 91
5. Some Elements on Levy Processes……Page 128
6. Iterated Random Maps and Some Classes of Markov Processes……Page 156
7. Random Walk and Fluctuation Theory……Page 182
8. A Semigroup Representation and Asymptotic Behavior of Certain Statistics of the Fisher-Wright-Moran Coalescent……Page 225
9. Continuous-Time ARMA Processes……Page 258
10. Record Sequences and their Applications……Page 286
11. Stochastic Networks with Product Form Equilibrium……Page 318
12. Stochastic Processes in Insurance and Finance……Page 374
13. Renewal Theory……Page 422
14. The Kolmogorov Isomorphism Theorem and Extensions to Some Nonstationary Processes……Page 451
15. Stochastic Processes in Reliability……Page 479
16. On the Supports of Stochastic Processes of Multiplicity One……Page 519
17. Gaussian Processes: Inequalities, Small Ball Probabilities and Applications……Page 540
18. Point Processes and Some Related Processes……Page 605
19. Characterization and Identifiability for Stochastic Processes……Page 648
20. Associated Sequences and Related Inference Problems……Page 697
21. Exchangeability, Functional Equations, and Characterizations……Page 736
22. Martingales and Some Applications……Page 767
23. Markov Chains: Structure and Applications……Page 819
24. Diffusion Processes……Page 854
25. Ito’s Stochastic Calculus and Its Applications……Page 874
Subject Index……Page 935
Handbook of Statistics: Contents of Previous Volumes……Page 947