Probability Theory and Mathematical Statistics. Vol. 1

Yu. V. Prohorov, V. A. Statulevičius, V. V. Sazonov, B. Grigelionis

• Publisher: De Gruyter
• Year: 2020
• ISBN:
  9783112319000
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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