| Exact Rate of Convergence of the Milstein Method for Fractional Stochastic Differential Equations |
| کد مقاله : 1079-FEMATH6 |
| نویسندگان |
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رامین آذری *1، امید فرخنده روز2، داوود احمدیان2 1دانشجوی دکتری تخصصی رشته ریاضیات کاربردی آنالیزعددی دانشگاه تبریز 2دانشکده علوم ریاضی دانشگاه تبریز |
| چکیده مقاله |
| In this paper, we first express the method of variable-order fractional stochastic differential equations with Poisson jump. In the following, we introduce the compensated Ito-Taylor expansion for the solution of jump-diffusion FSDEs. Nevertheless, the Milstein method has never been applied to fractional stochastic differential equations with Poisson jump, at least to the best of our knowledge. In the present paper, in order to fill this gap, we introduce the Milstein method for fractional stochastic differential equations with Poisson jump by some numerical integration technique and perform a mean-square convergence analysis of the proposed scheme. Finally, we study a variable-order fractional stochastic differential equation with Poisson jump driven by a multiplicative noise, which contains a non-Lipschitz weakly singular kernel with a variable order, and loses the convolution structure due to the introduction of the variable-order fractional differential operator. We proved the wellposedness and moment estimates of the problem. We also developed a generalized Milstein method for the problem and we proved the mean-square convergence rate by using the compensated Milstein method. |
| کلیدواژه ها |
| Compensated Milstein methods, Mean-square convergence, Variable-order fractional stochastic, Poisson jump |
| وضعیت: پذیرفته شده |