Probability Theory and Mathematical Statistics. Vol. 1

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