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

Frontmatter -- Contents -- Preface -- The low density limit and the quantum Poisson process -- Systems assisting in gathering and analysis of statistical data and adjustable to subject domains -- On the maximum of sums of random variables and the supremum for stable processes -- On the necessity of Cramér's condition in local limit theorems -- Markov random graphs and polygonal fields with Y-shaped nodes -- Probability measures on quantum logics and a non-commutative Choquet theory -- Convolution semigroups of instruments in quantum probability -- Stochastic posterior equations for quantum nonlinear filtering -- Diffusions and parabolic equations in principal bundles -- On Markov processes associated with a projective sequence of harmonic spaces -- Estimation of the tail of the spectral distribution by means of high level sojourn times -- Renormalization of Dyson's vector-valued hierarchical model at low temperatures -- Analitic functionals of stochastic processes and infinite dimensional oscillatory integrals -- Exponential inequalities for the distributions of von Mises and U-statistics -- Ergodicity and stability of Markov chains and of their generalizations. Multidimensional chains -- Event and time averages: The stationary case and the nonstationary case -- On the convergence of sums of independent random vectors normed by matrices -- CLT for families of integral functionals arising in solving the multidimensional Burgers Equation -- The Theory Of Dynamical Semigroups And Its Applications -- An approximation of integer-valued measures by generalized Poisson measures -- Lim inf results for the standardized empirical distribution function -- The smooth measures in Banach spaces and their smooth mappings -- Local invariance principle for i.i.d. random variables -- Conditionally positive definite functions on the coefficient algebra of a nonabelian group -- On the integrability of the maximum and the local properties of Gaussian fields -- On large deviation probabilities for the maximum likelihood estimators -- Functional integrals, a variational method and some problems of stochastical physics -- The law of the iterated logarithm and order statistics -- Martingales in non-life insurance -- Asymptotic Minimaxity Of Usual Goodness Of Fit Tests -- Les fonctions aléatoires à valeurs dans les espaces lusiniens et leurs modifications régulières -- Critical branching caused by interaction with point catalysts -- Statistical analysis and dating of the observations on which Ptolomy's "Almagest" star catalogue is based -- Global asymptotics of solutions of the first and second boundary value problems for Kolmogorov equation with small diffusion -- Hydrodynamic limit for Ginzburg¿Landau type continuum model -- Almost everywhere limit convergence of subsequences of powers -- On shot noise processes with long range dependence -- G-estimates of eigen-values of covariance matrices -- On large deviations for trimmed sums of independent random variables -- Random operator functions defined by stochastic differential equations -- Hellinger integrals and Hellinger processes for solutions of martingale problems -- On connection between the theory of branching processes and queueing theory -- Estimation Of Manova Eigenvalues -- On joint distributions of random elements with given mutual conditional distributions -- Improvement and generalization of Cramér¿Rao inequality for a filtered space -- Limit Theorems For Record Times -- On statistics of continuous Markov processes: semi- Markov approach -- Quantum stochastic flows -- Convergence Of The Stochastic Quantization Method -- Adaptive tests for minimax testing of nonparametic hypotheses -- A survey of the metric theory of continued fractions, fifty years after Doeblin's 1940 paper -- Boundary and entropy of random walks in random environment -- Non-linear law of large numbers and Gaussian fluctuation for star-like networks -- Asymptotic solution of inverse Kolmogorov equation for diff