Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 265, Issue 7, Pages 2921-2967Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.04.052
Keywords
Explicit scheme; Switching diffusion systems; Local Lipschitz condition; Strong convergence; Stability; Invariant measure
Categories
Funding
- National Natural Science Foundation of China [11171056, 11471071, 11671072]
- Natural Science Foundation of Jilin Province [20170101044JC]
- Education Department of Jilin Province [JJKH20170904KJ]
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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.
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