Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Yang, Hongfu¹  Li, Xiaoyue¹ 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

关键词: Explicit scheme;    Switching diffusion systems;    Local Lipschitz condition;    Strong convergence;    Stability;    Invariant measure;   

DOI  :  10.1016/j.jde.2018.04.052

来源: Elsevier

【 摘 要 】

Focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events, this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a Markov chain. Different kinds of easily implementable explicit schemes have been proposed to approximate the dynamical behaviors of switching diffusion systems with locally Lipschitz continuous drift and diffusion coefficients in both finite and infinite intervals. Without additional restriction conditions except those which guarantee the exact solutions possess their dynamical properties, the numerical solutions converge strongly to the exact solutions in finite horizon, moreover, realize the approximation of long-time dynamical properties including the moment boundedness, stability and ergodicity. Some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free