{"title":"Probabilistic analysis of vantage point trees","authors":"V. Bohun","doi":"10.15559/21-vmsta188","DOIUrl":"https://doi.org/10.15559/21-vmsta188","url":null,"abstract":"","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"5 6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81787575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A stochastic parabolic equation on [ 0 ,T ] × R driven by a general stochastic measure is considered. The averaging principle for the equation is established. The convergence rate is compared with other results on related topics.
{"title":"Averaging principle for the one-dimensional parabolic equation driven by stochastic measure","authors":"B. Manikin","doi":"10.15559/21-vmsta195","DOIUrl":"https://doi.org/10.15559/21-vmsta195","url":null,"abstract":"A stochastic parabolic equation on [ 0 ,T ] × R driven by a general stochastic measure is considered. The averaging principle for the equation is established. The convergence rate is compared with other results on related topics.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85265635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On path-dependent SDEs involving distributional drifts","authors":"A. Ohashi, Francesco G. Russo, Alan Teixeira","doi":"10.15559/21-vmsta197","DOIUrl":"https://doi.org/10.15559/21-vmsta197","url":null,"abstract":"","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"84 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83821608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A linear structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors are assumed known. Without normality assumptions, consistent estimators of model parameters are constructed and conditions for their asymptotic normality are given. The estimators are divided into two asymptotically independent groups.
{"title":"Estimation in a linear errors-in-variables model under a mixture of classical and Berkson errors","authors":"Mykyta Yakovliev, A. Kukush","doi":"10.15559/21-vmsta186","DOIUrl":"https://doi.org/10.15559/21-vmsta186","url":null,"abstract":"A linear structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors are assumed known. Without normality assumptions, consistent estimators of model parameters are constructed and conditions for their asymptotic normality are given. The estimators are divided into two asymptotically independent groups.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"89 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83866981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a continuous time nonlinear regression model the residual correlogram is considered as an estimator of the stationary Gaussian random noise covariance function. For this estimator the functional central limit theorem is proved in the space of continuous functions. The result obtained shows that the limiting sample continuous Gaussian random process coincides with the limiting process in the central limit theorem for standard correlogram of the random noise in the specified regression model.
{"title":"Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model","authors":"A. Ivanov, K. Moskvychova","doi":"10.15559/20-vmsta170","DOIUrl":"https://doi.org/10.15559/20-vmsta170","url":null,"abstract":"In a continuous time nonlinear regression model the residual correlogram is considered as an estimator of the stationary Gaussian random noise covariance function. For this estimator the functional central limit theorem is proved in the space of continuous functions. The result obtained shows that the limiting sample continuous Gaussian random process coincides with the limiting process in the central limit theorem for standard correlogram of the random noise in the specified regression model.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84137415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean, and extinction of the solution to the considered system.
{"title":"Long-time behavior of a nonautonomous stochastic predator–prey model with jumps","authors":"O. Borysenko, O. Borysenko","doi":"10.15559/21-VMSTA173","DOIUrl":"https://doi.org/10.15559/21-VMSTA173","url":null,"abstract":"It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean, and extinction of the solution to the considered system.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"106 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80431411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct fiveand three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for the ruin probability in the case of exponentially distributed premium and claim sizes. Finally, we analyze the accuracy of the approximations for some typical distributions of premium and claim sizes using statistical estimates obtained by the Monte Carlo methods.
{"title":"Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy","authors":"O. Ragulina","doi":"10.15559/20-vmsta157","DOIUrl":"https://doi.org/10.15559/20-vmsta157","url":null,"abstract":"We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct fiveand three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for the ruin probability in the case of exponentially distributed premium and claim sizes. Finally, we analyze the accuracy of the approximations for some typical distributions of premium and claim sizes using statistical estimates obtained by the Monte Carlo methods.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"159 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75968122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper the change of measures technique for compound mixed renewal processes, developed in Tzaninis & Macheras [24], is applied to the ruin problem in order to compute the ruin probability and to find upper and lower bounds for it.
{"title":"Applications of a change of measures technique for compound mixed renewal processes to the ruin problem","authors":"Spyridon M. Tzaninis","doi":"10.15559/21-vmsta192","DOIUrl":"https://doi.org/10.15559/21-vmsta192","url":null,"abstract":"In the present paper the change of measures technique for compound mixed renewal processes, developed in Tzaninis & Macheras [24], is applied to the ruin problem in order to compute the ruin probability and to find upper and lower bounds for it.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"22 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87531218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new, direct proof of the formulas for the conic intrinsic volumes of the Weyl chambers of types ${A_{n-1}}$, ${B_{n}}$ and ${D_{n}}$ is given. These formulas express the conic intrinsic volumes in terms of the Stirling numbers of the first kind and their B- and D-analogues. The proof involves an explicit determination of the internal and external angles of the faces of the Weyl chambers.
{"title":"Conic intrinsic volumes of Weyl chambers","authors":"Thomas Godland, Z. Kabluchko","doi":"10.15559/22-vmsta206","DOIUrl":"https://doi.org/10.15559/22-vmsta206","url":null,"abstract":"A new, direct proof of the formulas for the conic intrinsic volumes of the Weyl chambers of types ${A_{n-1}}$, ${B_{n}}$ and ${D_{n}}$ is given. These formulas express the conic intrinsic volumes in terms of the Stirling numbers of the first kind and their B- and D-analogues. The proof involves an explicit determination of the internal and external angles of the faces of the Weyl chambers.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88611545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.
{"title":"Subordinated compound Poisson processes of order k","authors":"A. Sengar, N. S. Upadhye","doi":"10.15559/20-vmsta165","DOIUrl":"https://doi.org/10.15559/20-vmsta165","url":null,"abstract":"In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"16 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89106926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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