{"title":"Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths","authors":"Antoine-Marie Bogso, M. Dieye, O. M. Pamen","doi":"10.3150/22-BEJ1555","DOIUrl":null,"url":null,"abstract":"In this work, we generalise the stochastic local time space integration introduced in \\cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter It\\^o formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bernoulli","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3150/22-BEJ1555","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
In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter It\^o formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.
在这项工作中，我们推广了\cite{Ei00}中引入的随机局部时间空间积分到布朗页的情况。 %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter Itô formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
