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  • 3 - Stochastic Differential Equations

  • Radek Erban, University of Oxford, S. Jonathan Chapman, University of Oxford
  • Book:
    Stochastic Modelling of Reaction–Diffusion Processes
    Published online:
    04 November 2019
    Print publication:
    30 January 2020, pp 59-94

  • 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.