Ergodyczne własności losowych układów dynamicznych ze skokami o intensywności zależnej od stanu

Abstract

In this PhD thesis, we analyze the asymptotics of the Markov operator, acting on Borel measures of a Polish space, determining the evolution of a distributions of time- homogeneous Markov chain, which describes the states immediately following the jumps of a certain piecewise-deterministic Markov process. Between any two consecutive jumps, this process evolves deterministically according to one of the semiflows, randomly selected among a finite number of available ones at the moment of jump. The jumps occur in a Poisson-like fashion with state-depentent rate, and each of them is attained by a continuous transformation of the pre-jump state, randomly drawn (with a place-dependent probability) from an arbitrarily given family of all possible ones.