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Stability and Strong Convergence for Spatial Stochastic Kinetics

In: Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

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  • Stefan Engblom

    (Uppsala University, Division of Scientific Computing, Department of Information Technology)

Abstract

We review conditions for the well-posedness of models of stochastic jump kinetics. Our focus is on obtaining bounds in the sense of mean square, implying in particular so-called strong convergence. We look especially on problems posed in a spatial setting, formed by merging a local reaction process with a connecting transport mechanism. This type of network jump process occurs naturally in many applications and is an attractive modeling framework, yet is a challenge from the perspective of numerical analysis. Since the stochastic modeling itself is motivated by the presence of nonlinear feedback terms, by small number of participating agents, and by an overall noisy environment, a consistent analysis framework is clearly required. The review summarizes the required mathematical framework and techniques used for obtaining a priori bounds and stability estimates.

Suggested Citation

  • Stefan Engblom, 2017. "Stability and Strong Convergence for Spatial Stochastic Kinetics," Springer Books, in: David Holcman (ed.), Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, pages 109-125, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62627-7_5
    DOI: 10.1007/978-3-319-62627-7_5
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