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Ergodic approximation to chemical reaction system with delay. (English) Zbl 1418.60049

Summary: In order to inherit numerically the ergodicity of the chemical reaction system with delays, we propose and study an Euler-type numerical method from the point of view of stochastic delay differential equations. We not only prove the unique exponential ergodicity of the numerical solution of the approximation, but also present error estimation on invariant measures, which gives order 1 under certain hypotheses. Numerical experiments are provided to illustrate the results.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
65C20 Probabilistic models, generic numerical methods in probability and statistics
65C30 Numerical solutions to stochastic differential and integral equations
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