Piecewise deterministic Markov processes in biological models

Abstract

We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induced by such Markov processes are applied to specific examples.

in: Semigroup of Operators - Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp. 235-255

References in corpus (1)

• Substochastic semigroups and densities of piecewise deterministic Markov processes

Cited by in corpus (3)

• Existence of invariant densities for semiflows with jumps
• Densities for piecewise deterministic Markov processes with boundary
• Nonparametric estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes