Probability Theory and Mathematical Statistics: Vol. 1 [Reprint 2020 ed.] 9783112319000, 9783112307878

Table of contents :
CONTENTS
Preface
Quantum stochastic calculus
Glivenko-Cantelli convergence for weighted empirical and quantile processes of U-statistic structure
On symmetry properties and nonparametric estimates of the ʋ-th order spectral density of a stationary random process
Large deviations for first-passage times
Quasi-average approach to the description of the limit states of the n-vector Curie-Weiss ferromagnet
Inequalities at the Markov approximation of lumped processes
Remarks on limit theorems for sequences of random variables with random index
Continuity of local time for Markov processes with stationary independent increments
Detection and diagnosis of changes in the A.R. part of an A.R.M. A. model with nonstationary unknown M. A. coefficients
Nonparametric estimation of distribution functions based on incomplete data
Diffusion processes on the group T ∞ and elliptic equations of infinitely many variables
Lower estimates of the convergence rate in the CLT in Banach spaces
Weak limits of probability measures on metric Schauderspaces
Optimal consumption and investment in a stochastic model
Large deviations from classical paths and the classical limit of quantum stochastic flows
Limit theorems for multicomponent hierarchical models
On limit theorems for random vectors controlled by a Markov chain
Upper and lower estimates of the convergence rate in the invariance principle for empirical measures
The contraction principle for C0-summing operators and SLLN for weighed sums
Limit theorems for stochastic inventory models
Limit theorems under weak dependence conditions
Non commutative integration and probability on von Neumann algebras
On optimal controls in the problem of locally absolutely continuous change of measure (compact sets of decisions)
Non-uniform estimates of the remainder term in limit theorems with a stable limit law
Multiple stable stochastic integrals
A generalization of p-type spaces
Smooth measures on infinite dimensional manifolds and forward Kolmogorov equation
The structure of distributions of convex functionals
Wiener germs applied to the tails of m-estimators
On the asymptotic behaviour of the linear stochastic heat equation solutions
Some universal donsker classes of functions
Duplicates in mixed sequences and a frequency duplication principle. Methods and applications
Bootstrapping empirical measures indexed by Vapnik-Chervonenkis classes of sets
A remark on the Central Limit Theorem for random measures and processes
Elliptic law and elements of G-analysis
Mathematical aspects on the variation of air pollutant concentrations
Weak solutions of the stochastic evolution and invariance principles
Optimal stopping of a Markov chain with vector-valued gain function
Some strong laws of large numbers in Banach spaces with regular norms
Optimality in estimation for stochastic processes under both fixed and large sample conditions
On urn schemes imbedded in birth processes
Limiting distributions and mean-values of complex-valued multiplicative functions
Asymptotically minimax testing of nonparametric hypotheses