Applications of stochastic semigroups to cell cycle models

DOI10.3934/DCDSB.2019099arXiv1806.00091WikidataQ128061955 ScholiaQ128061955MaRDI QIDQ6302391

Katarzyna Pichór, Ryszard Rundnicki

Publication date: 31 May 2018

Abstract: We consider a generational and continuous-time two-phase model of the cell cycle. The first model is given by a stochastic operator, and the second by a piecewise deterministic Markov process. In the second case we also introduce a stochastic semigroup which describes the evolution of densities of the process. We study long-time behaviour of these models. In particular we prove theorems on asymptotic stability and sweeping. We also show the relations between both models.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Cell biology (92C37)

This page was built for publication: Applications of stochastic semigroups to cell cycle models