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

被引：0
作者：
Kamrani, Minoo [1 ]
Debrabant, Kristian [2 ]
Jamshidi, Nahid [1 ]
机构：
[1] Razi Univ, Fac Sci, Dept Math, Kermanshah 6714115111, Iran
[2] Univ Southern Denmark, Dept Math & Comp Sci IMADA, Odense, Denmark
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2024年 / 101卷 / 03期
关键词：
Stiff stochastic differential equations; fractional Brownian motion; exponential Euler scheme; pathwise stability; STATIONARY SOLUTIONS; NUMERICAL APPROXIMATION; DRIVEN; CONVERGENCE; SYSTEMS; DISCRETIZATION; CALCULUS;
D O I：
10.1080/00207160.2024.2327615
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 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.
引用
收藏
页码：357 / 371
页数：15
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