Asymptotic Expansions for Singulary Perturbed Stochastic Differential Equations

Chapters in this book

1. Frontmatter I
2. CONTENTS V
3. Preface XIII
4. Bakuriani Colloquia on Probability Theory and Mathematical Statistics XV
5. I. LIMIT THEOREMS: FINITE - DIMENSIONAL CASE
6. On the Bounds for the Probabilities of Large Deviations for Random Variables and Vectors 1
7. The Influence of Extremes Summands on the Law of Iterated Logarithm 11
8. Generalized Marcinkiewicz's Theorem and Asymptotic Expansions in the Central Limit Theorem 30
9. On Integrability of sup [S_nk /n_k] 38
10. Asymptotic Expansions in Large Deviation Zones for the Distribution Density of Sums of Independent Random Variables 43
11. Strong Law of Large Numbers for Operator Normalized Sums of Independent Random Vectors 57
12. II. LIMIT THEOREMS IN GENERAL SPACES
13. On the Distribution of the Sup-Norm for a Stable Motion and the Rate of Convergence 73
14. Semi-Invariant Conditions of Weak Convergence of Random Processes in the Space of Continuous Functions 78
15. Almost Sure Permutational Convergence of Vector Random Series and Kolmogorov's Problem 93
16. Limit Theorems for Stable Laws in Banach Spaces 106
17. An Estimate of the Rate of Convergence in the CLT for Dependent Hilbert Space Valued Random Variables 111
18. An Improved Estimate of the Accuracy of Gaussian Approximation in Hilbert Space 123
19. On Laxge Deviations for L-Estimates 137
20. III. LIMIT THEOREMS FOR STOCHASTIC PROCESSES
21. Rates of Convergence in the Invariance Principle for Empirical Processes 167
22. Ergodic Theorem for Semimartingale-Helix 183
23. Ergodic Theorems for Discrete Time Random Processes 190
24. On Functional Principle of Large Deviations 198
25. IV. PROBABILITIES IN GENERAL SPACES
26. Some Properties of Gaussian Measures and Potentials in Martingale Spaces with Mixed Norm 221
27. Unexpected Limit Behaviour of the Gaussian Tail Probabilities 233
28. Topologies on the Space of a-Additive Cylindrical Probabilities 241
29. Two-Sided Exponential Inequalities for the Distribution of the Norm of Banach Space Valued Random Variables 246
30. Nonuniform Estimates of the Density of the Squared Norm of a Gaussian Vector in Hilbert Space 255
31. On Sequential Conditions for a Cylindrical Measure to be Countably Additive 264
32. A Family of Measures Admitting Consistent Estimates 276
33. V. STOCHASTIC ANALYSIS AND CONTROL
34. Asymptotic Behaviour of Solutions of Stochastic Equations 289
35. On the Decomposition of a Maximum of Semimartingales and Ito's Generalized Formula 301
36. Optimal Transmission of Gaussian Signals Involving Cost for Transmission and Feedback 351
37. Stationary and Periodic Solutions of Stochastic Difference and Differential Equations in Banach Space 375
38. Controlled Random Fields on Graphs and Stochastic Models of Economic Equilibrium 391
39. Asymptotic Expansions for Singulary Perturbed Stochastic Differential Equations 413
40. On Uniformly Optimal Coding of Gaussian Messages in White Gaussian Channels with Feedback 436
41. On the Structure of a Random Graph with Nonuniform Distribution 445
42. Identities for Ladder Functionals of Homogeneous Random Processes and Walks with Independent Increments 457
43. On Convergence of Solutions of Stochastic Equations 474
44. Stochastic Integrals and Stochastic Differential Equations on the Plane Involving Strong Semimartingales 485
45. Itó-Ventsel' Formula For Anticipative Processes 503
46. Connectivity Property and Optimality Almost Surely and in Probability 528
47. Absolute Continuity of Smooth Measures Generated by Nonlinear Equations 540
48. VI. MATHEMATICAL STATISTICS
49. A New Method of Asymptotic Analysis of Simple Linear Rank Statistics 553
50. On Stable M-Estimators in the Partial Likelihood Scheme 567
51. Asymptotic Estimation of Integrals of Certain Random Fields 597
52. On Minimax Bound for Parameter Estimation in Ball (Bias Accounting) 612
53. Limit Theorems for Some Random Processes Based on Frequencies 617
54. From Asymptotic Efficiency in Minimax Sense to Bahadur Efficiency 629
55. On Estimating Parameters of a Distribution Concentrated in a Circle 636
56. On the Approximation of the Likelihood Function by a Vector Analogue of the Whittle Statistics 644
57. VII. TOWARDS NATURAL SCIENCES
58. On Condensable Point Processes 655
59. The Ground State of a Random Stationary Medium in the Mean Field Approximation 668
60. Scaling Behavior of Random Walks with Topological Constraints 683
61. Convergence of the Stochastic Quantization Method for Lattice R-Gauge Theories 694
62. List of Contributors 701
63. Organizing Committee and Acknowledgement 702