{"title":"A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock–Williams equation","authors":"J. Jakubowski, Maciej Wiśniewolski","doi":"10.3150/20-BEJ1295","DOIUrl":null,"url":null,"abstract":"A new probabilistic insight into the structure of local time is presented. A convolution formula for the local time at 0 of Ito diffusions reflecting at 0 is obtained. A simple integro-differential equation for the cumulative distribution function of the local time is given. Finally, a probabilistic representation of a generalized Stroock–Williams equation is presented.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"27 1","pages":"1870-1898"},"PeriodicalIF":1.5000,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bernoulli","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3150/20-BEJ1295","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 3
Abstract
A new probabilistic insight into the structure of local time is presented. A convolution formula for the local time at 0 of Ito diffusions reflecting at 0 is obtained. A simple integro-differential equation for the cumulative distribution function of the local time is given. Finally, a probabilistic representation of a generalized Stroock–Williams equation is presented.
期刊介绍:
BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work.
BERNOULLI will publish:
Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed.
Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research:
Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments.
Scholarly written papers on some historical significant aspect of statistics and probability.