Approximations for adapted M-solutions of Type-II backward stochastic Volterra integral equations

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2021-02-17 DOI:10.1051/ps/2022017

Yushi Hamaguchi, Daichi Taguchi

引用次数: 3

Abstract

In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, we obtain two approximation results, namely, a BSDE approximation and a numerical approximation. The BSDE approximation means that the solution of a finite system of backward stochastic differential equations (BSDEs) converges to the adapted M-solution of the original equation. As a consequence of the BSDE approximation, we obtain an estimate for the $L^2$-time regularity of the adapted M-solutions of Type-II BSVIEs. For the numerical approximation, we provide a backward Euler--Maruyama scheme, and show that the scheme converges in the strong $L^2$-sense with the convergence speed of order $1/2$. These results hold true without any differentiability conditions for the coefficients.

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一类后向随机Volterra积分方程的自适应m解的逼近

本文研究了一类后向随机Volterra积分方程(BSVIEs)。对于所适应的m -解，我们得到了两个近似结果，即BSDE近似和数值近似。BSDE近似意味着有限倒向随机微分方程(BSDEs)的解收敛于原方程的自适应m解。作为BSDE近似的结果，我们得到了ii型BSVIEs的自适应m -解的$L^2$时间正则性的估计。对于数值逼近，我们给出了一个向后的Euler—Maruyama格式，并证明了该格式在强L^2 -意义下收敛，收敛速度为$1/2$阶。这些结果在系数没有可微条件的情况下成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.