Katarzyna Pichór

Markov Semigroups and Their Applications

Some recent results concerning asymptotic properties of Markov operators and semigroups are presented. Applications to diffusion processes and to randomly perturbed dynamical systems are given.

MARKOV SEMIGROUPS AND STABILITY OF THE CELL MATURITY DISTRIBUTION

A model of the maturity-structured cell population is considered. This model is described by a partial differential equation with a transformed argument. Using the theory of Markov semigroups we establish a new criterion for asymptotic stability of such equations.

Asymptotic decomposition of substochastic semigroups and applications

Theorems on asymptotic decomposition of substochastic semigroups are given. General results are applied to show asymptotic properties of substochastic semigroups generated by dynamical systems with random switching.

Stochastic semigroups and their applications to biological models

Abstract Some recent results concerning generation and asymptotic properties of stochastic semigroups are presented. The general results are applied to biological models described by piecewise deterministic Markov processes: birth-death processes, the evolution of the genome, genes expression and physiologically structured models.

Asymptotic behaviour of a structured population model

We consider a first order partial differential equation with a transformed argument which describes a model of the maturity-structured cell population. A new criterion for an asynchronous exponential growth of the solution to such an equation is given.