{"title":"Approximation and error analysis of forward-backward SDEs driven by general Lévy processes using shot noise series representations","authors":"Till Massing","doi":"10.1051/ps/2023013","DOIUrl":null,"url":null,"abstract":"We consider the simulation of a system of decoupled forward-backward stochastic differential\nequations (FBSDEs) driven by a pure jump Lévy process L and an independent Brownian motion\nB. We allow the Lévy process L to have an infinite jump activity. Therefore, it is necessary for the\nsimulation to employ a finite approximation of its Lévy measure. We use the generalized shot noise\nseries representation method by Rosiński (2001) to approximate the driving Lévy process L. We\ncompute the Lp error, p ≥ 2, between the true and the approximated FBSDEs which arises from\nthe finite truncation of the shot noise series (given sufficient conditions for existence and uniqueness\nof the FBSDE). We also derive the Lp error between the true solution and the discretization of the\napproximated FBSDE using an appropriate backward Euler scheme.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2023013","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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