用散点噪声序列表示一般lsamvy过程驱动的前后向SDEs的逼近和误差分析

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2021-08-10 DOI:10.1051/ps/2023013

Till Massing

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引用次数: 1

摘要

我们考虑了一个由纯跳跃过程L和独立布朗运动b驱动的解耦正反向随机微分方程系统的仿真。我们允许lsamvy过程L具有无限跳跃活动。因此，在模拟中有必要对其lsamvy测量值采用有限近似值。我们使用Rosiński(2001)的广义射击噪声序列表示方法来近似驱动lsamvy过程l。我们计算了由射击噪声序列有限截断引起的真实和近似FBSDE之间的Lp误差p≥2(给定FBSDE存在和唯一性的充分条件)。我们还利用适当的后向欧拉格式导出了近似FBSDE的真实解与离散化之间的Lp误差。

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Approximation and error analysis of forward-backward SDEs driven by general Lévy processes using shot noise series representations

We consider the simulation of a system of decoupled forward-backward stochastic differential equations (FBSDEs) driven by a pure jump Lévy process L and an independent Brownian motion B. We allow the Lévy process L to have an infinite jump activity. Therefore, it is necessary for the simulation to employ a finite approximation of its Lévy measure. We use the generalized shot noise series representation method by Rosiński (2001) to approximate the driving Lévy process L. We compute the Lp error, p ≥ 2, between the true and the approximated FBSDEs which arises from the finite truncation of the shot noise series (given sufficient conditions for existence and uniqueness of the FBSDE). We also derive the Lp error between the true solution and the discretization of the approximated FBSDE using an appropriate backward Euler scheme.

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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.