{"title":"Transportation of diffuse random measures on Rd","authors":"G. Last, H. Thorisson","doi":"10.30757/alea.v20-21","DOIUrl":null,"url":null,"abstract":"We consider two jointly stationary and ergodic random measures $\\xi$ and $\\eta$ on $\\mathbb{R}^d$ with equal finite intensities, assuming $\\xi$ to be diffuse. An allocation is a random mapping taking $\\mathbb{R}^d$ to $\\mathbb{R}^d\\cup\\{\\infty\\}$ in a translation invariant way. We construct allocations transporting the diffuse $\\xi$ to arbitrary $\\eta$, under the mild condition of existence of an `auxiliary' point process which is needed only in the case when $\\eta$ is diffuse. When that condition does not hold we show by a counterexample that an allocation transporting $\\xi$ to $\\eta$ need not exist.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v20-21","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 3
Abstract
We consider two jointly stationary and ergodic random measures $\xi$ and $\eta$ on $\mathbb{R}^d$ with equal finite intensities, assuming $\xi$ to be diffuse. An allocation is a random mapping taking $\mathbb{R}^d$ to $\mathbb{R}^d\cup\{\infty\}$ in a translation invariant way. We construct allocations transporting the diffuse $\xi$ to arbitrary $\eta$, under the mild condition of existence of an `auxiliary' point process which is needed only in the case when $\eta$ is diffuse. When that condition does not hold we show by a counterexample that an allocation transporting $\xi$ to $\eta$ need not exist.
期刊介绍:
ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted.
ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper.
ALEA is affiliated with the Institute of Mathematical Statistics.