Lectures on the Theory of Stochastic Processes /

Lectures on the Theory of Stochastic Processes / / Anatolij V. Skorochod.

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
VerfasserIn:
Skorochod, Anatolij V.,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2019]
©1996
Year of Publication:2019
Edition:Reprint 2018
Language:English
Online Access:
Physical Description:1 online resource (VI, 183 p.) :; Num. figs.
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Table of Contents:
  • Frontmatter
  • Contents
  • Preface
  • Lecture 1. Stochastic processes. definitions. examples
  • Lecture 2. The kolmogorov consistency theorem. classification of processes
  • Lecture 3. Random walks. recurrence. renewal theorem
  • Lecture 4. Martingales. inequalities for martingales
  • Lecture 5. Theorems on the limit of a martingale
  • Lecture 6. Stationary sequences. ergodic theorem
  • Lecture 7. Ergodic theorem. metric transitivity
  • Lecture 8. Regularization of a process. continuity
  • Lecture 9. Processes without discontinuities of the second kind
  • Lecture 10. Continuity of processes with independent increments. martingales with continuous time
  • Lecture 11. Measurable processes
  • Lecture 12. Stopping times. associated tr-algebras
  • Lecture 13. Completely measurable processes
  • Lecture 14. L2-theory
  • Lecture 15. Stochastic integrals
  • Lecture 16. Stationary processes. spectral representations
  • Lecture 17. Stationary sequences. regularity and singularity
  • Lecture 18. The prediction of a stationary sequence
  • Lecture 19. Markov processes
  • Lecture 20. Homogeneous markov processes and associated semigroups
  • Lecture 21. Homogeneous purely discontinuous processes. conditions for their regularity
  • Lecture 22. Processes with adenumerable set of states
  • Lecture 23. Simple birth and death processes
  • Lecture 24. Branching processes with particles of only one kind
  • Lecture 25. Homogeneous processes and strongly continuous semigroups. resolvent operator and generator
  • Lecture 26. The hille-iosida theorem
  • Lecture 27. Processes with independent increments. representation of the discontinuous part
  • Lecture 28. General representation of a stochastically continuous process with independent increments
  • Lecture 29. Diffusion processes
  • Lecture 30. Stochastic integrals
  • Lecture 31. Existence, uniqueness, and properties of solutions of stochastic differential equations
  • Lecture 32. Itô's formula with some corollaries
  • Bibliography

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