一类遍历跳跃扩散的不变分布的近似

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI:10.1051/PS/2020023

A. Gloter, Igor Honoré, D. Loukianova

{"title":"一类遍历跳跃扩散的不变分布的近似","authors":"A. Gloter, Igor Honoré, D. Loukianova","doi":"10.1051/PS/2020023","DOIUrl":null,"url":null,"abstract":"In this article, we approximate the invariant distributionνof an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps. This scheme is similar to those introduced in Lamberton and PagèsBernoulli8(2002) 367-405. for a Brownian diffusion and extended in F. Panloup,Ann. Appl. Probab.18(2008) 379-426. to a diffusion with Lévy jumps. We obtain a non-asymptoticquasiGaussian (asymptotically Gaussian) concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functionsfsuch thatf−ν(f) is a coboundary of the infinitesimal generator.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"8 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Approximation of the invariant distribution for a class of ergodic jump diffusions\",\"authors\":\"A. Gloter, Igor Honoré, D. Loukianova\",\"doi\":\"10.1051/PS/2020023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we approximate the invariant distributionνof an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps. This scheme is similar to those introduced in Lamberton and PagèsBernoulli8(2002) 367-405. for a Brownian diffusion and extended in F. Panloup,Ann. Appl. Probab.18(2008) 379-426. to a diffusion with Lévy jumps. We obtain a non-asymptoticquasiGaussian (asymptotically Gaussian) concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functionsfsuch thatf−ν(f) is a coboundary of the infinitesimal generator.\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/PS/2020023\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/PS/2020023","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: 3

摘要

在本文中，我们近似了由布朗运动和亚高斯跳变的复合泊松过程和驱动的遍历跳变扩散的不变量分布。首先构造了一种时间步长递减的欧拉离散格式。该方案与Lamberton和pagautisbernoulli8(2002) 367-405中引入的方案类似。张建平，张建平。一类布朗扩散及其推广。达成。Probab.18(2008) 379 - 426。到与lsamvy跳跃的扩散。我们得到了不变分布与经验分布之差的一个非渐近拟高斯(渐近高斯)浓度界，该分布采用沿适当的测试函数递减时间步长格式计算，使得f−ν(f)是无穷小发生器的共边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Approximation of the invariant distribution for a class of ergodic jump diffusions

In this article, we approximate the invariant distributionνof an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps. This scheme is similar to those introduced in Lamberton and PagèsBernoulli8(2002) 367-405. for a Brownian diffusion and extended in F. Panloup,Ann. Appl. Probab.18(2008) 379-426. to a diffusion with Lévy jumps. We obtain a non-asymptoticquasiGaussian (asymptotically Gaussian) concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functionsfsuch thatf−ν(f) is a coboundary of the infinitesimal generator.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.