{"title":"Some expansion theorems for stochastic processes. II.","authors":"Hirohisa Hatori","doi":"10.2996/KMJ/1138844783","DOIUrl":null,"url":null,"abstract":"which has been treated by Kawata [3] for r=Q and a =1/2 with somewhat different conditions, and extended by the author [1] for r=Q, 1, 2, ••• and 0^<*<1 with the above conditions (i)— (v). In this paper, we shall show (1.1) for X(t)=f(t)+φ(t)8(t), where φ(u) is a numerical valued function. If 0(s)>0, — oo<s<oo, then, for this process X(t\\ the correlation coefficient of X(t) and X(s) is a function of t— s only. In section 2, Taylor expansion of 8(t) is discussed and, in section 3, the expansion theorem for Γ χ(t-—}dH(s) J-oo \\ n / is given, where X(t)=f(t)+φ(f)8(t), -oo<t<oo.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1963-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Seminar Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2996/KMJ/1138844783","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
which has been treated by Kawata [3] for r=Q and a =1/2 with somewhat different conditions, and extended by the author [1] for r=Q, 1, 2, ••• and 0^<*<1 with the above conditions (i)— (v). In this paper, we shall show (1.1) for X(t)=f(t)+φ(t)8(t), where φ(u) is a numerical valued function. If 0(s)>0, — oo