Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise
Probability
2024-05-10 v2 Numerical Analysis
Numerical Analysis
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 H>1/2, 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, M.G. Riedler, and P.E. Kloeden 2011), we conclude the existence of a unique stationary solution of the exponential Euler scheme that is pathwise asymptotically stable.
Keywords
Cite
@article{arxiv.2308.13224,
title = {Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise},
author = {Minoo Kamrani and Kristian Debrabant and Nahid Jamshidi},
journal= {arXiv preprint arXiv:2308.13224},
year = {2024}
}