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Structure-preserving discretization of the chemical master equation. (English) Zbl 1378.65032

Authors’ abstract: The chemical master equation is a differential equation to model stochastic reaction systems. Its solutions are nonnegative and \(\ell^1\)-contractive which is inherently related to their interpretation as probability densities. In this note, numerical discretizations of arbitrarily high order are discussed and analyzed that preserve both of these properties simultaneously and without any restriction on the discretization parameters.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
80A30 Chemical kinetics in thermodynamics and heat transfer
60J27 Continuous-time Markov processes on discrete state spaces
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness

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