Resumen de Asymptotic behaviour of stochastic semigroups

Esther Dopazo

• The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.

  An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour of the iterations of stochastic operators is analyzed in the second section. And then it is applied to study asymptotic properties of stochastic semigroups.