{"title":"ehrenfest - brillouin型相关连续时间随机漫步和分数阶Jacobi扩散","authors":"N. Leonenko, I. Papic, A. Sikorskii, N. Šuvak","doi":"10.1090/TPMS/1086","DOIUrl":null,"url":null,"abstract":"Continuous time random walks (CTRWs) have random waiting times between particle \njumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated \nCTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of \nJacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW \nconsidered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not \na L´evy process but a diffusion process with non-independent increments. The waiting times between \njumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with \nthese waiting times converge to Y (E(t)).","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/TPMS/1086","citationCount":"1","resultStr":"{\"title\":\"Ehrenfest–Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion\",\"authors\":\"N. Leonenko, I. Papic, A. Sikorskii, N. Šuvak\",\"doi\":\"10.1090/TPMS/1086\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Continuous time random walks (CTRWs) have random waiting times between particle \\njumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated \\nCTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of \\nJacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW \\nconsidered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not \\na L´evy process but a diffusion process with non-independent increments. The waiting times between \\njumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with \\nthese waiting times converge to Y (E(t)).\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/TPMS/1086\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/TPMS/1086\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/TPMS/1086","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Ehrenfest–Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion
Continuous time random walks (CTRWs) have random waiting times between particle
jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated
CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of
Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW
considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not
a L´evy process but a diffusion process with non-independent increments. The waiting times between
jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with
these waiting times converge to Y (E(t)).