{"title":"初值为δ的抛物型Anderson模型的一个几乎确定的中心极限定理","authors":"Jingyu Li, Yong Zhang","doi":"10.1080/17442508.2022.2088236","DOIUrl":null,"url":null,"abstract":"Consider the parabolic Anderson model of the form , where for t>0 and with , and η is a centered Gaussian noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure f that satisfies Dalang's condition. Let denote the standard Gaussian heat kernel on and set for all t>0 and . In this paper, we present an almost sure central limit theorem (ASCLT) and a functional ASCLT for spatial averages of the form as for fixed t>0 based on the quantitative analysis of f. In particular, when f is given by a Riesz kernel, that is, for some , we can also obtain the ASCLT.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"483 - 500"},"PeriodicalIF":1.1000,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"An almost sure central limit theorem for the parabolic Anderson model with delta initial condition\",\"authors\":\"Jingyu Li, Yong Zhang\",\"doi\":\"10.1080/17442508.2022.2088236\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider the parabolic Anderson model of the form , where for t>0 and with , and η is a centered Gaussian noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure f that satisfies Dalang's condition. Let denote the standard Gaussian heat kernel on and set for all t>0 and . In this paper, we present an almost sure central limit theorem (ASCLT) and a functional ASCLT for spatial averages of the form as for fixed t>0 based on the quantitative analysis of f. In particular, when f is given by a Riesz kernel, that is, for some , we can also obtain the ASCLT.\",\"PeriodicalId\":50447,\"journal\":{\"name\":\"Finance and Stochastics\",\"volume\":\"1 1\",\"pages\":\"483 - 500\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finance and Stochastics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2022.2088236\",\"RegionNum\":2,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/17442508.2022.2088236","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
An almost sure central limit theorem for the parabolic Anderson model with delta initial condition
Consider the parabolic Anderson model of the form , where for t>0 and with , and η is a centered Gaussian noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure f that satisfies Dalang's condition. Let denote the standard Gaussian heat kernel on and set for all t>0 and . In this paper, we present an almost sure central limit theorem (ASCLT) and a functional ASCLT for spatial averages of the form as for fixed t>0 based on the quantitative analysis of f. In particular, when f is given by a Riesz kernel, that is, for some , we can also obtain the ASCLT.
期刊介绍:
The purpose of Finance and Stochastics is to provide a high standard publication forum for research
- in all areas of finance based on stochastic methods
- on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance.
Finance and Stochastics encompasses - but is not limited to - the following fields:
- theory and analysis of financial markets
- continuous time finance
- derivatives research
- insurance in relation to finance
- portfolio selection
- credit and market risks
- term structure models
- statistical and empirical financial studies based on advanced stochastic methods
- numerical and stochastic solution techniques for problems in finance
- intertemporal economics, uncertainty and information in relation to finance.