The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations
| Autor: | Junhao Hu, Guoting Song, Shuaibin Gao, Xiaoyue Li |
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| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Numerical analysis Probability (math.PR) 010103 numerical & computational mathematics Delay differential equation Numerical Analysis (math.NA) 01 natural sciences Stability (probability) 010101 applied mathematics Moment (mathematics) Nonlinear system Rate of convergence Bounded function Convergence (routing) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.2008.08249 |
| Popis: | This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under less restrictive conditions, the truncated Euler-Maruyama (TEM) schemes for SDDEs are proposed, which numerical solutions are bounded in the q th moment for q ≥ 2 and converge to the exact solutions strongly in any finite interval. The 1/2 order convergence rate is yielded. Furthermore, the long-time asymptotic behaviors of numerical solutions, such as stability in mean square and $\mathbb {P}-1$ , are examined. Several numerical experiments are carried out to illustrate our results. |
| Databáze: | OpenAIRE |
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