Speciality:
01.01.05 (Probability theory and mathematical statistics)
Birth date:
30.12.1946
E-mail: Keywords: branching processes,
discrete probability problems,
probabilistic inequalities,
applications of discrete probability.
Subject:
Nesessary and sufficient conditions for almost sure extinction of bounded branching processes were established for discrete and for continuous time. Limit theorems were proved for:
a) $\varphi$–branching processes, b) critical decomposable branching processes with two types of particles and infinite second moments of offsprings,
c) distance to the nearest mutual ancestor of all simultaneously existing particles in a branching process,
d) conditional distributions of the number of particles on the life spans of branching process with immigration.
Limit distributions of a statistical estimate for the entropy of the polynomial distribution with growing number of outcomes were described. Explicit estimates of the rate of convergence of renewal density were found. Limit theorems and inequalities for distributions of random variables related with repeating tuples of outcomes in iid sequence were proved (in joint papers with V. G. Mihailov). Explicit inequalities for the accuracy of Poisson or compound Poisson approximations for the distributions of sums of functions of independent random variables were obtained. Explicit inequalities for taboo probabilities in Markov chains; these inequalities were used in the proofs of limit theorems for the time to the first occurence of rare event and for the frequencies of outcomes in a trajectories of discrete Markov chains with growing state space. A method to prove probabilistic inequalities by means of quadratic forms was elaborated and applied to the probabilities of the union of events, to the moments of ratios of positive random variables, to the generating functions and to the Laplace transforms.
