Probability Theory and Mathematical Statistics. Vol. 1 (PDF)

Frontmatter -- 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 ?-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