Pub Date : 2023-10-09DOI: 10.1080/07362994.2023.2262551
Silvia Sabatini, Elena Villa
Abstract.Inspired by issues of formal kinetics in materials science, we consider a class of processes with density with respect to an inhomogeneous finite Poisson point process, which may be regarded as a generalization of the classical Strauss hard-core process. We prove expressions for the intensity measure and the void probabilities, together with upper and lower bounds. A discussion on some special cases of interest, links with literature and a comparison between Matérn I and Strauss hard-core process are also provided. We apply such a special class of point processes in modeling patterns of non-overlapping grains and in the study of the mean volume density of particular birth-and-growth processes.Keywords: Gibbs hard-core point processintensitygerm-grain modelmean volume densityAMS Classification 2020:: 60G5560D05 AcknowledgmentsThe authors would like to thank Harison S. Ventura for the figures, and Professor P.R. Rios of Universidade Federal Fluminense for fruitful discussions on application problems.EV is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).Disclosure statementThe authors report there are no competing interests to declare.
摘要受材料科学中形式动力学问题的启发，我们考虑了一类关于非齐次有限泊松点过程的密度过程，该过程可视为经典施特劳斯硬核过程的推广。我们证明了强度测度和空洞概率的表达式，以及上界和下界。还讨论了一些特殊的感兴趣的案例，与文献的联系，以及matsamrn I和Strauss硬核过程之间的比较。我们将这类特殊的点过程应用于非重叠晶粒模式的建模以及特定出生和生长过程的平均体积密度的研究。关键词:Gibbs硬核点工艺强度细菌颗粒模型平均体积密度ams分类2020::60G5560D05致谢作者要感谢Harison S. Ventura提供的数据，以及联邦佛罗里达大学P.R. Rios教授对应用问题的富有成效的讨论。EV是意大利国家数学研究所(INdAM)下属的数学分析、概率和应用国家小组(GNAMPA)的成员。作者报告无利益竞争需要申报。
{"title":"On a special class of gibbs hard-core point processes modeling random patterns of non-overlapping grains","authors":"Silvia Sabatini, Elena Villa","doi":"10.1080/07362994.2023.2262551","DOIUrl":"https://doi.org/10.1080/07362994.2023.2262551","url":null,"abstract":"Abstract.Inspired by issues of formal kinetics in materials science, we consider a class of processes with density with respect to an inhomogeneous finite Poisson point process, which may be regarded as a generalization of the classical Strauss hard-core process. We prove expressions for the intensity measure and the void probabilities, together with upper and lower bounds. A discussion on some special cases of interest, links with literature and a comparison between Matérn I and Strauss hard-core process are also provided. We apply such a special class of point processes in modeling patterns of non-overlapping grains and in the study of the mean volume density of particular birth-and-growth processes.Keywords: Gibbs hard-core point processintensitygerm-grain modelmean volume densityAMS Classification 2020:: 60G5560D05 AcknowledgmentsThe authors would like to thank Harison S. Ventura for the figures, and Professor P.R. Rios of Universidade Federal Fluminense for fruitful discussions on application problems.EV is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).Disclosure statementThe authors report there are no competing interests to declare.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141668","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 : 2023-09-13DOI: 10.1080/07362994.2023.2254371
Amali Paul Rose Gregory, Murugan Suvinthra, Krishnan Balachandran
In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm.
{"title":"Large deviation principle for the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise","authors":"Amali Paul Rose Gregory, Murugan Suvinthra, Krishnan Balachandran","doi":"10.1080/07362994.2023.2254371","DOIUrl":"https://doi.org/10.1080/07362994.2023.2254371","url":null,"abstract":"In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135733629","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 : 2023-07-04DOI: 10.1080/07362994.2022.2075385
Nguyen Tien Dung, Ta Cong Son
Abstract The problem of investigating the continuity in the Hurst index arises naturally in statistical inferences related to fractional Brownian motion. In this paper, based on the techniques of the Malliavin calculus, we introduce a method to deal with this problem. We first provide an explicit bound on the difference between two non-smooth functionals of Malliavin differentiable random variables. Then, we apply the obtained bound to show Lipchitz continuity of fractional stochastic Volterra integro-differential equations and its additive functionals.
{"title":"Lipschitz continuity in the Hurst index of the solutions of fractional stochastic volterra integro-differential equations","authors":"Nguyen Tien Dung, Ta Cong Son","doi":"10.1080/07362994.2022.2075385","DOIUrl":"https://doi.org/10.1080/07362994.2022.2075385","url":null,"abstract":"Abstract The problem of investigating the continuity in the Hurst index arises naturally in statistical inferences related to fractional Brownian motion. In this paper, based on the techniques of the Malliavin calculus, we introduce a method to deal with this problem. We first provide an explicit bound on the difference between two non-smooth functionals of Malliavin differentiable random variables. Then, we apply the obtained bound to show Lipchitz continuity of fractional stochastic Volterra integro-differential equations and its additive functionals.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"693 - 712"},"PeriodicalIF":1.3,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46069548","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 : 2023-05-29DOI: 10.1080/07362994.2023.2213745
P. Jordanova, M. Stehlík
{"title":"Flexible extreme value inference","authors":"P. Jordanova, M. Stehlík","doi":"10.1080/07362994.2023.2213745","DOIUrl":"https://doi.org/10.1080/07362994.2023.2213745","url":null,"abstract":"","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48661709","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 : 2023-05-08DOI: 10.1080/07362994.2023.2208654
Gerardo Hernández-del-Valle, Wincy A. Guerra-Polania
{"title":"On the heat equation with a moving boundary and applications to hitting times for Brownian motion","authors":"Gerardo Hernández-del-Valle, Wincy A. Guerra-Polania","doi":"10.1080/07362994.2023.2208654","DOIUrl":"https://doi.org/10.1080/07362994.2023.2208654","url":null,"abstract":"","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42297528","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 : 2023-05-02DOI: 10.1080/07362994.2023.2203733
Hani Abidi, Abdelkarim Oualaid, Y. Ouknine, R. Pettersson
{"title":"A mild approach to spatial discretization for backward stochastic differential equations in infinite dimensions","authors":"Hani Abidi, Abdelkarim Oualaid, Y. Ouknine, R. Pettersson","doi":"10.1080/07362994.2023.2203733","DOIUrl":"https://doi.org/10.1080/07362994.2023.2203733","url":null,"abstract":"","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47889500","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 : 2023-04-12DOI: 10.1080/07362994.2023.2192267
{"title":"Stochastic calculus for tempered fractional Brownian motion and stability for SDEs driven by TFBM","authors":"","doi":"10.1080/07362994.2023.2192267","DOIUrl":"https://doi.org/10.1080/07362994.2023.2192267","url":null,"abstract":"","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48310445","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 : 2023-03-17DOI: 10.1080/07362994.2023.2242471
P. Jordanova, Mladen Savov, Assen Tchorbadjieff, Milan Stehl'ik
Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular cases. Homogeneous Poisson processes are appropriate apriori models for the number of renewals up to a given time $t>0$. This paper mixes them and considers a Mixed Poisson process with Stacy mixing variable. We call it a Poisson-Stacy process. The resulting counting process is one of the Generalised Negative Binomial processes, and the distribution of its time-intersections are very-well investigated in the scientific literature. Here we define and investigate their joint probability distributions. Then, the corresponding mixed renewal process is investigated and Exp-Stacy and Erlang-Stacy distributions are defined and partially studied. The paper finishes with a simulation study of these stochastic processes. Some plots of the probability density functions, probability mass functions, mean square regressions and sample paths are drawn together with the corresponding code for the simulations.
{"title":"Mixed Poisson process with Stacy mixing variable","authors":"P. Jordanova, Mladen Savov, Assen Tchorbadjieff, Milan Stehl'ik","doi":"10.1080/07362994.2023.2242471","DOIUrl":"https://doi.org/10.1080/07362994.2023.2242471","url":null,"abstract":"Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular cases. Homogeneous Poisson processes are appropriate apriori models for the number of renewals up to a given time $t>0$. This paper mixes them and considers a Mixed Poisson process with Stacy mixing variable. We call it a Poisson-Stacy process. The resulting counting process is one of the Generalised Negative Binomial processes, and the distribution of its time-intersections are very-well investigated in the scientific literature. Here we define and investigate their joint probability distributions. Then, the corresponding mixed renewal process is investigated and Exp-Stacy and Erlang-Stacy distributions are defined and partially studied. The paper finishes with a simulation study of these stochastic processes. Some plots of the probability density functions, probability mass functions, mean square regressions and sample paths are drawn together with the corresponding code for the simulations.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45496048","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 : 2023-02-01DOI: 10.1080/07362994.2023.2170885
N. Flournoy, L. Hearne, J. Kiseľák, M. Stehlík
{"title":"On dose-response modeling for evaluation of drugs combinations","authors":"N. Flournoy, L. Hearne, J. Kiseľák, M. Stehlík","doi":"10.1080/07362994.2023.2170885","DOIUrl":"https://doi.org/10.1080/07362994.2023.2170885","url":null,"abstract":"","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47607481","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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