On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps. (English) Zbl 1382.65021
Summary: This paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps. By the Itô formula, stochastic inequality and semi-martingale convergence theorem, we study the asymptotic stability in the \(p\)th moment and almost sure exponential stability of solutions under the local Lipschitz condition and nonlinear growth condition. On the other hand, we also show the convergence in probability of numerical schemes under nonlinear growth condition. Finally, an example is provided to illustrate the theory.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34D20 | Stability of solutions to ordinary differential equations |
| 60J75 | Jump processes (MSC2010) |
| 93E15 | Stochastic stability in control theory |
Keywords:
Poisson random measure; nonlinear stochastic differential equations; asymptotic stability; numerical analysisReferences:
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