Strong convergence of Numerical Methods for Nonlinear Stochastic DifferentialnEquations with Jumps
کد مقاله : 1049-FEMATH-FULL (R1)
نویسندگان:
1حمیده نسب زاده *، 2یاسر طاهری نسب
1هیئت علمی تمام وقت
2دانشجو
چکیده مقاله:
Numerical methods applied to SDEs with jump require a global Lipschitz assumption .Many important SDE with jump models satisfy only a local Lipschitz property.nnD. Higham and Peter E. Kloeden‎ presented and analyzed two implicit methods for nSDEs with Poisson-driven jumps.nThe first method, SSBE, is a split-step extension of the backwardnEuler method. The second method, CSSBE, arises from the introductionnof a compensated, martingale, form of the Poisson process.nThey showed that both methods are amenable to rigorous analysis whenna one-sided Lipschitz condition, rather than a more restrictive globalnLipschitz condition, holds for the drift. Their analysis covers strongnconvergence and nonlinear stability. they proved that both methods givenstrong convergence when the drift coefficient is one-sided Lipschitznand the diffusion and jump coefficients are globally Lipschitz. nnX. Mao and Lukasz Szpruch proved strong convergence results under less restrictive conditions.nAs an application of this general theory they showed that if the diffusion coefficient is globally Lipschitz,n but the drift coefficient satisfies only a one-sidednLipschitz condition; this is achieved by showing that the implicit method has bounded moments andnmay be viewed as an Euler-Maruyama approximation to a perturbed SDE of the same form.nnnIn this paper we extend this conditions that presents by Mao and Szpruch, to SDEs with jumps, i.e. we prove the strong convergence of SSBE and CSSBE methods for the SDEs with jumps, when the drift coefficient is one-sided Lipschitznand the diffusion and jump coefficients are globally Lipschitz.
کلیدواژه ها:
One-sided Lipschitz condition; Poisson process; Stochastic differential equation with jump,Strong convergence.
وضعیت : مقاله برای ارائه شفاهی پذیرفته شده است