{"title":"Cox-Ingersoll-Ross过程的运行最大值与Kummer函数的一些性质","authors":"S. Gerhold, F. Hubalek, R. Paris","doi":"10.54379/jiasf-2022-2-1","DOIUrl":null,"url":null,"abstract":"We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.","PeriodicalId":43883,"journal":{"name":"Journal of Inequalities and Special Functions","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function\",\"authors\":\"S. Gerhold, F. Hubalek, R. Paris\",\"doi\":\"10.54379/jiasf-2022-2-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.\",\"PeriodicalId\":43883,\"journal\":{\"name\":\"Journal of Inequalities and Special Functions\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Special Functions\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54379/jiasf-2022-2-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Special Functions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54379/jiasf-2022-2-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function
We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.
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