Probability Theory and Mathematical Statistics (PDF)

Frontmatter -- CONTENTS -- PREFACE -- Large deviations in approximation by Poisson law -- Limits of weak interaction for stochastic particle system -- Rate of convergence in the limit transfer theorem of the maximum and minimum -- Geometry of the state spaces in quantum probability -- From diffusions to processes with jumps -- Central limit theorem in Skorohod spaces and asymptotic strength distribution of fiber bundles -- Ergodicity in a sense of weak convergence, equilibrium-type identities and large deviations for Markov chains -- On second-order properties of mixing random sequences and random fields -- Optimal couplings and application to Riemannian geometry -- Empirical and partial sum processes with sample path in Banach function spaces -- Applications of multi-time parameter processes to change-point analysis -- Bergström-type asymptotic expansions in the first uniform Kolmogorov's theorem -- Differentiation of heat semigroups and applications -- On the realisation of classical Markov processes as quantum flows in Fock space -- Unimodular eigenvalues and invariant probabilities for some classes of linear operators -- On function-indexed partial-sum processes -- Canonical spectral equation for the eigenvalues of empirical covariance matrices -- Conditionally exponential families and Lundberg exponents of Markov additive processes -- On the nonuniform approximation by means of distributions of sums of conditionally independent random variables -- Kolmogorov's strong law of large numbers: the amart point of view -- Cycle processes -- Density-dependent branching processes as randomly perturbed iterations of maps -- Stability of the inverse Radon transform -- On conditions for existence of solutions of integral equations with stochastic line integrals -- Nonlinear transformations of empirical processes: functional inverses and Bahadur-Kiefer representations -- Rate of convergence in the functional central limit theorem for one-dimensional semimartingales -- On limit theorems for the Riemann zeta-function in some spaces -- A posteriori and sequential methods of change-point detection in FARIMA-type time series -- Limit theorems for the local density of measures in the hypotheses testing problems of counting processes -- On the strong independence of sequential ranks -- A proof of the Erdös arcsine law -- Quasi-state decompositions for quantum spin systems -- On accuracy of approximation with stable laws -- Distributions of processes governed by hyperbolic equations when also boundary conditions are assumed -- Central limit theorems on stratified Lie groups -- On the convergence rate in the multi-dimensional martingale CLT -- Stein-Chen method for compound Poisson approximation: the coupling approach -- Some aspects of the development of probabilistic number theory -- Mixture of extremal distributions - a model alternative to the log-linear model -- Infinite-dimensional M-estimation -- On large deviations in averaging principle for systems of stochastic differential equation with unbounded coefficients