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Pathwise error bounds in multiscale variable splitting methods for spatial stochastic kinetics. (English) Zbl 1382.65013

Summary: Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models, the computational complexity can be rather high such that approximate multiscale models are attractive alternatives. Within this framework some variables are described stochastically, while others are approximated with a macroscopic point value. We devise theoretical tools for analyzing the pathwise multiscale convergence of this type of variable splitting methods, aiming specifically at spatially extended models. Notably, the conditions we develop guarantee well-posedness of the approximations without requiring explicit assumptions of a priori bounded solutions. We are also able to quantify the effect of the different sources of errors, namely, the multiscale error and the splitting error, respectively, by developing suitable error bounds. Computational experiments on selected problems serve to illustrate our findings.

MSC:

65C20 Probabilistic models, generic numerical methods in probability and statistics
92E20 Classical flows, reactions, etc. in chemistry
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
60J27 Continuous-time Markov processes on discrete state spaces
65Y20 Complexity and performance of numerical algorithms

Software:

Hy3S; URDME
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Full Text: DOI arXiv

References:

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