{"title":"逆首次通过时间问题的唯一性和Shiryaev边界的形状","authors":"A. Klump, M. Kolb","doi":"10.1137/s0040585x97t991155","DOIUrl":null,"url":null,"abstract":"Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary\",\"authors\":\"A. Klump, M. Kolb\",\"doi\":\"10.1137/s0040585x97t991155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t991155\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991155","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary
Given a distribution on the positive extended real line, the two-sided inverse first-passage time problem for Brownian motion asks for a function such that the first passage time of this function by a reflected Brownian motion has the given distribution. We combine the ideas of Ekström and Janson, which were developed within the scope of the one-sided inverse first-passage time problem, with the methods of De Masi et al., which were used in the context of free boundary problems, in order to give a different proof for the uniqueness for the two-sided inverse first-passage time problem by using a stochastic order relation. We provide criteria for qualitative properties of solutions of the inverse first-passage problem, which apply to the boundary corresponding to the exponential distribution.