CONVERGENCE AND STABILITY OF MODIFIED FULLY IMPLICIT MILSTEIN SCHEME FOR STOCHASTIC DIFFERENTIALEQUATIONS
عنوان مقاله: CONVERGENCE AND STABILITY OF MODIFIED FULLY IMPLICIT MILSTEIN SCHEME FOR STOCHASTIC DIFFERENTIALEQUATIONS
شناسه ملی مقاله: ICBVPA01_055
منتشر شده در اولین کنفرانس بین المللی مسائل مقدار مرزی و کاربردها در سال 1397
شناسه ملی مقاله: ICBVPA01_055
منتشر شده در اولین کنفرانس بین المللی مسائل مقدار مرزی و کاربردها در سال 1397
مشخصات نویسندگان مقاله:
O Farkhondeh Rouz
D Ahmadian
A.A Jodayree Akbarfam
خلاصه مقاله:
O Farkhondeh Rouz
D Ahmadian
A.A Jodayree Akbarfam
Abstract. In this paper we discuss implicit Taylor methods for It^o stochastic differ-ential equations (SDEs). Based on the relationship between It^o stochastic integrals andbackward stochastic integrals, presented two implicit Taylor methods: the implicit Euler-Taylor method with strong order p = 0:5, and the implicit Milstein-Taylor method withstrong order p = 1. The main purpose of this paper is to study the convergence andmean-square stability of a new class of modi ed fully implicit Milstein (MFIM) methodfor solving systems of It^o SDEs. This paper concludes that the MFIM method withtwo parameters θ, ηЄ [0; 1] converge strongly to the exact solution with order p = 1, alsoinvestigates mean-square stability properties of these two implicit Taylor and the MFIMmethods. We combine analytical and numerical techniques to get insights into the stabil-ity properties. Finally, numerical results are reported to illustrate the convergence andstability results.
کلمات کلیدی: Mean-square stability, Convergence, Modi ed fully implicit Milstein method, Stochastic differential equation
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/801136/