On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching

被引：8

作者：

Kumar, Chaman ^{[1
]}

Kumar, Tejinder ^{[1
]}

机构：

[1] Indian Inst Technol Roorkee, Dept Math, Roorkee, Uttarakhand, India

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 377卷

关键词：

Markovian switching; Tamed Milstein-type scheme; Rate of strong convergence; Super-linear coefficient; EULER APPROXIMATIONS; VARYING COEFFICIENTS; NUMERICAL-SOLUTIONS; DIFFUSION; CONVERGENCE; SDES; FINITE; TIME;

D O I：

10.1016/j.cam.2020.112917

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a new tamed Milstein-type scheme for stochastic differential equation with Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate of convergence is shown to be equal to 1.0 under mild regularity (e.g. once differentiability) requirements on drift and diffusion coefficients. Novel techniques are developed to tackle two-fold difficulties arising due to jumps of the Markov chain and the reduction of regularity requirements on the coefficients. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：24

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