Probability Theory and Applications

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Frontmatter -- Contents -- Preface -- Greeting -- Opening Talk -- Algorithms And Randomness -- Self Similar Processes In Probability Theory And Statistics (Session 9 - Chairman: Ya.G. Sinay) -- INVITED PAPERS -- Limit theorems in statistical physics; on Dyson's hierarchical model -- Statistical aspects of self-similar processes -- Toeplitz matrices and estimation of time series with long-range dependence -- Contributed Papers -- Universal behavior and stochasticity for one dimensional systems -- A birth and death process in random environment -- Spectral properties of some finite-difference and differential operators with random coefficients -- Point Processes In Probability Theory And Statistics (Session 10 - Chairman: D. Stoyan) -- Invited Papers -- Parametric and non-parametric estimation for pairwise-interaction point processes -- On the theory of conditioning in point processes -- Contributed Papers -- On The Exponentiality Of Total Hazards Before Failure -- Sufficient regularity conditions for jump processes -- Statistics with diffusion crossing times -- Ruin probabilities in the "non-renewal" case -- A note on the asymptotic behaviour of the empirical score in Cox's regression model for counting processes -- Comparison of Cox's and maximum likelihood estimates for matched experiments in survival data with censoring -- On the conditions providing for the moments of number of zeros of a vector Gaussian field to be finite -- The inverses of thinned point processes -- Foundations Of Probability Theory (Session 17 - Chairman: D. Lane) -- Invited Papers -- An epistemic justification of the law of total probability -- Contributed Papers -- Individual Random Continuous Functions -- Some Estimates For Nonstochastic Sequences -- Nonstandard Analysis In Probability Theory (Session 19 - Chairman: E. Perkins) -- Invited Papers -- Nonstandard Constructions Of Diffusions And Related Processes -- Nonstandard analysis in probability theory -- Contributed Papers -- Adapted distribution -- Hyperfinite methods for multidimensional stochastic processes -- Combinatorial Methods In Probability Theory (Session 20 - Chairman: B.S. Stechkin) -- Invited Papers -- Random mappings and branching processes -- On probability methods in combinatorial analysis -- Contributed Papers -- Neighbourhood Spaces And Maps -- Percolation theory. Coincidence of the critical values PH = PT -- Evolution on random mappings -- On the distribution of the number of vertices in strata of a random forest -- Queing Theory (Network, Computer-User Models, Stability ...) (Session 22 - Chairman: R. Schassberger) -- Invited Papers -- Stationary queueing systems. Existence and stability -- Ergodicity and asymptotic behaviour of multi-type branching processes arising in random-access communication systems -- Insensitive service schemes and partial balance -- Contributed Papers -- Queueing networks and operator-selfdecomposability -- Insensitivity in queueing networks with generalized processor-sharing discipline -- Markov Processes (Session 24 - Chairman: Y. Le Jan) -- Invited Papers -- Intrinsic properties of Markov processes -- Reversible diffusion processes on manifolds -- The entropy production and reversibility of Markov processes -- Contributed Papers -- The theory of shuffling - an application of non-homogeneous Markov chains -- Asymptotic periodicity of the iterates of Markov operators -- Homogeneous transition functions and dual semigroups -- On the arcsine law in the adaptive control of Markov chains -- Random Fields And Percolation Theory (Session 25 - Chairman: Y. Higuchi) -- Invited Papers -- Random sets and Markov fields -- Central limit results for random fields -- Recent progress in percolation -- Contributed Papers -- Uniqueness of Gibbs measures and absorption probabilities -- A decomposition theorem for binary Markov random fields -- Percolation problem for the two-dimensional Ising model -- Probabilistic models of the growth of epithelial tumors -- On the homogenization error for boundary problems with highly oscillating random coefficients -- Time Evolution Of Particle Systems (Session 26 - Chairman: T. Liggett) -- Invited Papers -- Switching networks, Markov interaction processes, Gibbsian fields - interconnection -- Collective behaviour of interacting particle systems -- Contributed Papers -- The supremum of a random walk in a Markovian environment -- Dynamics of infinite particle systems and Gibbs point random fields -- The Euler equations for the one-dimensional zero range process -- Probability And Theoretical Physics (Session 27 - Chairman: K.R. Parthasarathy) -- Invited Papers -- Recent developments in quantum probability -- Markov operators on quantum probability spaces -- Some recent interactions between mathematics and physics in connection with generalized random fields -- Contributed Papers -- Non-commutative point processes and quantum kinetic equations -- Quantum diffusions and cohomology of algebras -- Quantum stochastic calculus with integral kernels I -- Quantum stochastic calculus with integral kernels II: the Wigner-Weisskopf atom -- Stop Times in Fock Space Stochastic Calculus -- Diffusion On Manifolds (Session 28 - Chairman: K.D. Elworthy) -- Invited Papers -- Some Geometric Aspects Of Diffusions On Manifolds -- Stochastic Differential Geometry -- Contributed Papers -- Stochastic equations on Banach manifolds and bundles -- Brownian motion in a small ball -- Stochastic Calculus (Including Malliavin Calculus) (Session 29 - Chairman: J. Bismut) -- Invited Papers -- Stochastic quantization: A new domain for stochastic analysis -- Some intersection properties of Brownian paths and random walks -- Malliavin calculus and its application to some limit theorems -- Contributed Papers -- Probabilistic method of approach to certain problems of Fourier analysis -- On sufficient conditions for the convergence of solutions of stochastic equations -- Martingales with mixed norm: general theory and applications -- Convergence in probability for solutions of stochastic differential equations -- Some remarks on approximation of predictable characteristics of processes with filtrations -- Stochastic Geometry (Session 30 - Chairman: J. Mecke) -- Invited Papers -- Stochastic approximations of convex bodies by polyhedrons -- Symmetric statistics and random shape -- Point processes of compact sets -- Contributed Papers -- A brief account of the structure and explicit determination of convex-polygonally generated shape-densities -- On homogeneous processes of lines in the plane -- Intersections of random curves and surfaces -- Random curvature currents and generalized Regge calculus -- Large Deviations (Session 31 - Chairman: A.A. Borovkov) -- Invited Papers -- Theorems of large deviations for multinomial forms and multiple stochastic integrals -- Global exact asymptotics of large deviations probabilities for diffusion and jump processes -- Contributed Papers -- Large deviations and long-time behavior of stochastic particle systems -- Random perturbations of infinite dimensional dynamical systems -- Large deviations estimates for systems with small (wideband) noise effects and applications to stochastic systems and conmunication theory -- On the Donsker-Varadhan theory and its applications -- Rates Of Convergence (Session 32 - Chairman: F. Götze) -- Invited Papers -- Approximations in functional limit theorems -- Asymptotic expansions refining the central limit theorem in Hilbert space -- Contributed Papers -- Estimates of the rate of convergence in the local limit theorem for countable Markov chains -- On asymptotic expansion for the distribution of the sum of independent identically distributed random variables taking values in Hilbert space -- On the uniform approximation of distribution functions of sums of independent non-identically distributed random variables -- Functional Limit Theorems: An Invariance Principle (Session 33 - Chairman: Yu.V. Prohorov) -- Invited Papers -- On accuracy of approximation in invariance principle -- Contributed Papers -- On strong convergence of distributions of random process functionals -- Almost sure invariance principles for generalization of martingales -- On the rate of convergence in ordinary and functional central limit theorems for martingales -- Probabilities On Algebraic Structures (Session 34 - Chairman: V.M. Maksimov) -- Invited Papers -- Generalized convolutions and probability theory based on the q-Heisenberg algebra -- Asymptotic behaviour of products of random matrices -- Lie algebraic methods in filtering and identification -- Contributed Papers -- Limit theorem for products of dependence -- Random series and seminorms -- Miscellaneous (Session 35) -- Contributed Papers -- On the maximum principle for stochastic control problems -- Stochastic scheduling via stochastic control -- A de Finetti theorem for a class of pairwise independent stationary processes -- Computer application in the teaching process at the institute of economics -- Probabilistic derivation of inversion formulas