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Summary

This chapter introduces stochastic differential equations (SDEs) from the computational point of view, starting with several examples to illustrate the computational definition of the SDE that is used throughout the book. The Fokker–Planck and Kolmogorov backward equations are then derived and their consequences presented. They are used to compute the mean transition time between favourable states of SDEs. The SDE formalism is then applied to a chemical system by deriving the chemical Fokker–Planck equation and the corresponding chemical Langevin equation. They are used to further analyse the chemical systems from Chapter 2, including the system with multiple favourable states and the self-induced stochastic resonance.

This note is motivated by Blom's work in 1989. We consider a generalized Ehrenfest urn model in which a randomly-chosen ball has a positive probability of moving from one urn to the other urn. We use recursion relations between the mean transition times to derive formulas in terms of finite sums, which are shown to be equivalent to the definite integrals obtained by Blom.

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3 - Stochastic Differential Equations

Summary

A note on a generalized Ehrenfest urn model: another look at the mean transition times

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2 results

3 - Stochastic Differential Equations

Summary

A note on a generalized Ehrenfest urn model: another look at the mean transition times