نظریه احتمال و آمار ریاضی. جلد ۱ ۲۰۲۰
Probability Theory and Mathematical Statistics. Vol. 1 2020

1. CONTENTS

2. Preface

3. Quantum stochastic calculus

4. Glivenko-Cantelli convergence for weighted empirical and quantile processes of U-statistic structure

5. On symmetry properties and nonparametric estimates of the ʋ-th order spectral density of a stationary random process

6. Large deviations for first-passage times

7. Quasi-average approach to the description of the limit states of the n-vector Curie-Weiss ferromagnet

8. Inequalities at the Markov approximation of lumped processes

9. Remarks on limit theorems for sequences of random variables with random index

10. Continuity of local time for Markov processes with stationary independent increments

11. Detection and diagnosis of changes in the A.R. part of an A.R.M. A. model with nonstationary unknown M. A. coefficients

12. Nonparametric estimation of distribution functions based on incomplete data

13. Diffusion processes on the group T ^∞ and elliptic equations of infinitely many variables

14. Lower estimates of the convergence rate in the CLT in Banach spaces

15. Weak limits of probability measures on metric Schauderspaces

16. Optimal consumption and investment in a stochastic model

17. Large deviations from classical paths and the classical limit of quantum stochastic flows

18. Limit theorems for multicomponent hierarchical models

19. On limit theorems for random vectors controlled by a Markov chain

20. Upper and lower estimates of the convergence rate in the invariance principle for empirical measures

21. The contraction principle for C₀-summing operators and SLLN for weighed sums

22. Limit theorems for stochastic inventory models

23. Limit theorems under weak dependence conditions

24. Non commutative integration and probability on von Neumann algebras

25. On optimal controls in the problem of locally absolutely continuous change of measure (compact sets of decisions)

26. Non-uniform estimates of the remainder term in limit theorems with a stable limit law

27. Multiple stable stochastic integrals

28. A generalization of p-type spaces

29. Smooth measures on infinite dimensional manifolds and forward Kolmogorov equation

30. The structure of distributions of convex functionals

31. Wiener germs applied to the tails of m-estimators

32. On the asymptotic behaviour of the linear stochastic heat equation solutions

33. Some universal donsker classes of functions

34. Duplicates in mixed sequences and a frequency duplication principle. Methods and applications

35. Bootstrapping empirical measures indexed by Vapnik-Chervonenkis classes of sets

36. A remark on the Central Limit Theorem for random measures and processes

37. Elliptic law and elements of G-analysis

38. Mathematical aspects on the variation of air pollutant concentrations

39. Weak solutions of the stochastic evolution and invariance principles

40. Optimal stopping of a Markov chain with vector-valued gain function

41. Some strong laws of large numbers in Banach spaces with regular norms

42. Optimality in estimation for stochastic processes under both fixed and large sample conditions

43. On urn schemes imbedded in birth processes

44. Limiting distributions and mean-values of complex-valued multiplicative functions

45. Asymptotically minimax testing of nonparametric hypotheses