Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations
Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations
复制标题
II型后向随机Volterra积分方程自适应M解的近似
DOI：
10.1051/ps/2022017
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Taguchi Dai
中科院分区：
文献类型：
--
作者：
Hamaguchi Yushi;Taguchi Dai
在本文中，我们研究了一类 II 型后向随机 Volterra 积分方程（BSVIE）。对于适应的M-解，我们得到两个近似结果，即BSDE近似和数值近似。 BSDE 近似意味着向后随机微分方程 (BSDE) 的有限系统的解收敛到原始方程的自适应 M 解。作为 BSDE 近似的结果，我们获得了对 II 型 BSVIE 的自适应 M 解的 L2 时间规律性的估计。对于数值逼近，我们提供了后向Euler-Maruyama格式，并表明该格式在strongL2意义下收敛，收敛速度为1/2阶。这些结果在系数没有任何可微分条件的情况下成立。
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 theL2-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 strongL2-sense with the convergence speed of order 1/2. These results hold true without any differentiability conditions for the coefficients.