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May 9, 2026Theory of Probability and Its Applications0 citations

Euler Scheme for Some SDEs with Fractional Noise and Markov Switching

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HAH. ArayaJGJ. GarzónSTS. Torres

Key Points

  • This research aims to explore numerical approximations for stochastic differential equations influenced by fractional noise and Markov switching.
  • Utilized the Euler scheme for numerical approximation of SDEs driven by fractional Brownian motion.
  • Analyzed both additive and multiplicative noise cases, focusing on strong convergence in finite time intervals.
  • Conducted simulations to demonstrate the practical applications of theoretical results.
  • Established a convergence rate for the Euler scheme in the context of the studied SDEs.
  • Demonstrated strong convergence properties of the scheme in finite time intervals.
  • Provided simulation results that validate the theoretical convergence rates.

Abstract

We consider the numerical approximation by means of the Euler scheme of the unique solution to a class of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with Hurst parameter H (1/2, 1) and a Markov switching (MS). We first study the d-dimensional additive case, followed by a one-dimensional equation with multiplicative noise. The strong convergence of the scheme in a finite time interval is studied and a convergence rate is obtained. Some simulations are provided to show the application of the theoretical results.

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Cite This Study

Araya et al. (2026) studied this question.

synapsesocial.com/papers/69fecfafb9154b0b82876988https://doi.org/10.1137/s0040585x97t99277x
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