Applications of stochastic semigroups to cell cycle models

Katarzyna Pichór; Ryszard Rudnicki

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arXiv · 1806.00091

Applications of stochastic semigroups to cell cycle models

Katarzyna Pichór·Ryszard Rudnicki

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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.

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Katarzyna Pichór, Ryszard Rudnicki. 2018-05-31. Applications of stochastic semigroups to cell cycle models. https://arxiv.org/abs/1806.00091

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