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Stability and strong convergence in multiscale methods for spatial stochastic kinetics

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SDBW04 - Spatially distributed stochastic dynamical systems in biology

Co-authors: Pavol Bauer (Uppsala university), Augustin Chevallier (ENS Cachan), Stefan Widgren (National Veterinary Institute)

Recent progress in spatial stochastic modeling within the reaction-transport framework will be reviewed. I will first look at the issues with guaranteeing well-posedness of the involved mathematical and numerical models. Armed with this and the Lax-principle, I will then present an analysis of split-step methods and multiscale approximations, all performed in a pathwise, or “strong” sense. These analytical techniques hint at how effective (i.e. parallel) numerical implementations can be designed.

Some fairly large-scale simulations will serve as illustrations of the inherent flexibility of the modeling framework. While much of the initial motivation for this work came from problems in cell biology, I will also highlight examples from epidemics and neuroscience.

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