The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients

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Abstract

The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method are proved and the convergence of the numerical invariant measure to the underlying one is shown. Simulations are provided to illustrate the theoretical results and demonstrate the application of our results in the area of system control.
Original languageEnglish
Pages (from-to)137-150
Number of pages14
JournalApplied Numerical Mathematics
Volume184
Early online date14 Oct 2022
DOIs
Publication statusE-pub ahead of print - 14 Oct 2022

Keywords

  • stochastic differential equationquation
  • stationary measure
  • super-linear coefficients
  • Backward Euler-Maruyama method
  • implicit method

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