مباحثات در نظریه فرآیندهای تصادفی ۲۰۱۹
Lectures on the Theory of Stochastic Processes 2019

1. Contents

2. Preface

3. Lecture 1. Stochastic processes. definitions. examples

4. Lecture 2. The kolmogorov consistency theorem. classification of processes

5. Lecture 3. Random walks. recurrence. renewal theorem

6. Lecture 4. Martingales. inequalities for martingales

7. Lecture 5. Theorems on the limit of a martingale

8. Lecture 6. Stationary sequences. ergodic theorem

9. Lecture 7. Ergodic theorem. metric transitivity

10. Lecture 8. Regularization of a process. continuity

11. Lecture 9. Processes without discontinuities of the second kind

12. Lecture 10. Continuity of processes with independent increments. martingales with continuous time

13. Lecture 11. Measurable processes

14. Lecture 12. Stopping times. associated tr-algebras

15. Lecture 13. Completely measurable processes

16. Lecture 14. L2-theory

17. Lecture 15. Stochastic integrals

18. Lecture 16. Stationary processes. spectral representations

19. Lecture 17. Stationary sequences. regularity and singularity

20. Lecture 18. The prediction of a stationary sequence

21. Lecture 19. Markov processes

22. Lecture 20. Homogeneous markov processes and associated semigroups

23. Lecture 21. Homogeneous purely discontinuous processes. conditions for their regularity

24. Lecture 22. Processes with adenumerable set of states

25. Lecture 23. Simple birth and death processes

26. Lecture 24. Branching processes with particles of only one kind

27. Lecture 25. Homogeneous processes and strongly continuous semigroups. resolvent operator and generator

28. Lecture 26. The hille-iosida theorem

29. Lecture 27. Processes with independent increments. representation of the discontinuous part

30. Lecture 28. General representation of a stochastically continuous process with independent increments

31. Lecture 29. Diffusion processes

32. Lecture 30. Stochastic integrals

33. Lecture 31. Existence, uniqueness, and properties of solutions of stochastic differential equations

34. Lecture 32. Itô's formula with some corollaries

35. Bibliography