Pub Date : 2023-07-28DOI: 10.1007/s10959-023-01276-3
Huanchao Zhou, Jiang Hu, Zhidong Bai, Jack W. Silverstein
In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix.
{"title":"Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices","authors":"Huanchao Zhou, Jiang Hu, Zhidong Bai, Jack W. Silverstein","doi":"10.1007/s10959-023-01276-3","DOIUrl":"https://doi.org/10.1007/s10959-023-01276-3","url":null,"abstract":"In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the “general information-plus-noise\" type, as studied in Zhou (JTP 36:1203–1226, 2023). Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix.","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134966447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-30DOI: 10.1007/s10959-023-01270-9
J. Owo, A. Aman
{"title":"Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients","authors":"J. Owo, A. Aman","doi":"10.1007/s10959-023-01270-9","DOIUrl":"https://doi.org/10.1007/s10959-023-01270-9","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44152052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1007/s10959-023-01261-w
V. Kargin
{"title":"Scaling Limits of Slim and Fat Trees","authors":"V. Kargin","doi":"10.1007/s10959-023-01261-w","DOIUrl":"https://doi.org/10.1007/s10959-023-01261-w","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45442333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.1007/s10959-023-01269-2
E. Coffie, X. Mao, F. Proske
{"title":"On the Analysis of Ait-Sahalia-Type Model for Rough Volatility Modelling","authors":"E. Coffie, X. Mao, F. Proske","doi":"10.1007/s10959-023-01269-2","DOIUrl":"https://doi.org/10.1007/s10959-023-01269-2","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44238315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-07DOI: 10.1007/s10959-023-01266-5
N. Durga, P. Muthukumar
{"title":"Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps","authors":"N. Durga, P. Muthukumar","doi":"10.1007/s10959-023-01266-5","DOIUrl":"https://doi.org/10.1007/s10959-023-01266-5","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43070015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-24DOI: 10.1007/s10959-023-01258-5
Christian Bender, Joachim Lebovits, J. Lévy véhel
{"title":"General Transfer Formula for Stochastic Integral with Respect to Multifractional Brownian Motion","authors":"Christian Bender, Joachim Lebovits, J. Lévy véhel","doi":"10.1007/s10959-023-01258-5","DOIUrl":"https://doi.org/10.1007/s10959-023-01258-5","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49361159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-24DOI: 10.1007/s10959-023-01265-6
Jingjun Guo, Cuiyun Zhang, Aiqin Ma
{"title":"Derivative of Multiple Self-intersection Local Time for Fractional Brownian Motion","authors":"Jingjun Guo, Cuiyun Zhang, Aiqin Ma","doi":"10.1007/s10959-023-01265-6","DOIUrl":"https://doi.org/10.1007/s10959-023-01265-6","url":null,"abstract":"","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47731490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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