Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise

Minoo Kamrani*, Kristian Debrabant, Nahid Jamshidi

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter (Formula presented.), which arise e.g. from spatial approximations of stochastic partial differential equations. For their numerical approximation, we present an exponential Euler scheme and show that it converges in the strong sense with an exact rate close to the Hurst parameter H. Further, based on E. Buckwar et al. [The numerical stability of stochastic ordinary differential equations with additive noise, Stoch. Dyn. 11 (2011), pp. 265–281], we conclude the existence of a unique stationary solution of the exponential Euler scheme that is pathwise asymptotically stable.

Original languageEnglish
JournalInternational Journal of Computer Mathematics
Volume101
Issue number3
Pages (from-to)357-371
ISSN0020-7160
DOIs
Publication statusPublished - 2024

Keywords

  • 60H35
  • 65C30
  • exponential Euler scheme
  • fractional Brownian motion
  • pathwise stability
  • Stiff stochastic differential equations

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