{"title":"On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold","authors":"Fuzhou Gong, Xiaoxia Sun","doi":"10.3150/21-bej1420","DOIUrl":null,"url":null,"abstract":"In this paper, we focus on the characterization of a Brownian bridge measure on the pinned path space over a compact Riemannian manifold. In the case when the Riemannian manifold is simply connected, we prove that the integration by parts formula can characterize the Brownian bridge measure. Otherwise, we show that it is not always true by constructing an illustrating example.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bernoulli","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3150/21-bej1420","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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Abstract
In this paper, we focus on the characterization of a Brownian bridge measure on the pinned path space over a compact Riemannian manifold. In the case when the Riemannian manifold is simply connected, we prove that the integration by parts formula can characterize the Brownian bridge measure. Otherwise, we show that it is not always true by constructing an illustrating example.
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.
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