Stability and Strong Convergence for Spatial Stochastic Kinetics

  • Stefan EngblomEmail author


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.


Well-posedness Continuous-time Markov chain Network jump process Perturbation Rate equation Mean square bounds 

Mathematics Subject Classification (2010)

60J27 60J28 92C42 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Division of Scientific Computing, Department of Information TechnologyUppsala University05 UppsalaSweden

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