Probabilistic and Piecewise Deterministic models in Biology
arXiv:1706.09163 · doi:10.1051/proc/201760225
Abstract
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (1984), are a very general class of Markov processes and are being increasingly popular in biological applications. They also give new interesting challenges from the theoretical point of view. We give here different examples on the long time behavior of switching Markov models applied to population dynamics, on uniform sampling in general branching models applied to structured population dynamic, on time scale separation in integrate-and-fire models used in neuroscience, and, finally, on moment calculus in stochastic models of gene expression.
arXiv commentProceedings of the journées MAS 2016, session Probabilistic and Piecewise Deterministic models in Biology
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- Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes
- Markovian tricks for non-Markovian trees: contour process, extinction and scaling limits
- Application of the interacting particle system method to piecewise deterministic Markov processes used in reliability
- Piecewise deterministic sampling with splitting schemes
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