{"title":"分数阶布朗运动驱动随机微分方程的轨迹拟合估计","authors":"Hector Araya, John Barrera","doi":"10.1515/rose-2023-2018","DOIUrl":null,"url":null,"abstract":"Abstract We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>H</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {H\\in(\\frac{1}{2},1)} and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion\",\"authors\":\"Hector Araya, John Barrera\",\"doi\":\"10.1515/rose-2023-2018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:mi>H</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:mo stretchy=\\\"false\\\">(</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo stretchy=\\\"false\\\">)</m:mo> </m:mrow> </m:mrow> </m:math> {H\\\\in(\\\\frac{1}{2},1)} and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.\",\"PeriodicalId\":43421,\"journal\":{\"name\":\"Random Operators and Stochastic Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Operators and Stochastic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/rose-2023-2018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2023-2018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Trajectory fitting estimation for stochastic differential equations driven by fractional Brownian motion
Abstract We consider the problem of drift parameter estimation in a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H∈(12,1) {H\in(\frac{1}{2},1)} and small diffusion. The technique that we used is the trajectory fitting method. Strong consistency and asymptotic distribution of the estimator are established as a small diffusion coefficient goes to zero.
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