Smooth measures on infinite dimensional manifolds and forward Kolmogorov equation

Chapters in this book

1. Frontmatter I
2. CONTENTS V
3. Preface IX
4. Quantum stochastic calculus 1
5. Glivenko-Cantelli convergence for weighted empirical and quantile processes of U-statistic structure 23
6. On symmetry properties and nonparametric estimates of the ʋ-th order spectral density of a stationary random process 31
7. Large deviations for first-passage times 39
8. Quasi-average approach to the description of the limit states of the n-vector Curie-Weiss ferromagnet 69
9. Inequalities at the Markov approximation of lumped processes 85
10. Remarks on limit theorems for sequences of random variables with random index 99
11. Continuity of local time for Markov processes with stationary independent increments 115
12. Detection and diagnosis of changes in the A.R. part of an A.R.M. A. model with nonstationary unknown M. A. coefficients 119
13. Nonparametric estimation of distribution functions based on incomplete data 123
14. Diffusion processes on the group T ^∞ and elliptic equations of infinitely many variables 145
15. Lower estimates of the convergence rate in the CLT in Banach spaces 171
16. Weak limits of probability measures on metric Schauderspaces 189
17. Optimal consumption and investment in a stochastic model 199
18. Large deviations from classical paths and the classical limit of quantum stochastic flows 203
19. Limit theorems for multicomponent hierarchical models 211
20. On limit theorems for random vectors controlled by a Markov chain 231
21. Upper and lower estimates of the convergence rate in the invariance principle for empirical measures 251
22. The contraction principle for C₀-summing operators and SLLN for weighed sums 269
23. Limit theorems for stochastic inventory models 291
24. Limit theorems under weak dependence conditions 307
25. Non commutative integration and probability on von Neumann algebras 327
26. On optimal controls in the problem of locally absolutely continuous change of measure (compact sets of decisions) 331
27. Non-uniform estimates of the remainder term in limit theorems with a stable limit law 357
28. Multiple stable stochastic integrals 363
29. A generalization of p-type spaces 375
30. Smooth measures on infinite dimensional manifolds and forward Kolmogorov equation 385
31. The structure of distributions of convex functionals 405
32. Wiener germs applied to the tails of m-estimators 411
33. On the asymptotic behaviour of the linear stochastic heat equation solutions 419
34. Some universal donsker classes of functions 433
35. Duplicates in mixed sequences and a frequency duplication principle. Methods and applications 439
36. Bootstrapping empirical measures indexed by Vapnik-Chervonenkis classes of sets 467
37. A remark on the Central Limit Theorem for random measures and processes 483
38. Elliptic law and elements of G-analysis 489
39. Mathematical aspects on the variation of air pollutant concentrations 509
40. Weak solutions of the stochastic evolution and invariance principles 513
41. Optimal stopping of a Markov chain with vector-valued gain function 523
42. Some strong laws of large numbers in Banach spaces with regular norms 529
43. Optimality in estimation for stochastic processes under both fixed and large sample conditions 535
44. On urn schemes imbedded in birth processes 543
45. Limiting distributions and mean-values of complex-valued multiplicative functions 547
46. Asymptotically minimax testing of nonparametric hypotheses 553