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Theory of Probability and Mathematical Statistics最新文献

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On martingale solutions of stochastic partial differential equations with Lévy noise 带lsamvy噪声的随机偏微分方程的鞅解
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1147
V. Mandrekar, U. Naik-Nimbalkar
{"title":"On martingale solutions of stochastic partial differential equations with Lévy noise","authors":"V. Mandrekar, U. Naik-Nimbalkar","doi":"10.1090/tpms/1147","DOIUrl":"https://doi.org/10.1090/tpms/1147","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48040928","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}
引用次数: 24
On existence and uniqueness of the solution for stochastic partial differential equations 随机偏微分方程解的存在唯一性
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1144
B. Avelin, L. Viitasaari
{"title":"On existence and uniqueness of the solution for stochastic partial differential equations","authors":"B. Avelin, L. Viitasaari","doi":"10.1090/tpms/1144","DOIUrl":"https://doi.org/10.1090/tpms/1144","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43406816","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}
引用次数: 0
Extrapolation of stationary random fields via level sets 通过水平集的平稳随机场外推
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-08-27 DOI: 10.1090/tpms/1166
Abhinav B. Das, Vitalii Makogin, E. Spodarev
{"title":"Extrapolation of stationary random fields via level sets","authors":"Abhinav B. Das, Vitalii Makogin, E. Spodarev","doi":"10.1090/tpms/1166","DOIUrl":"https://doi.org/10.1090/tpms/1166","url":null,"abstract":"In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric difference of these sets under the condition that the univariate distributions of the predictor and of the field itself coincide. We illustrate the new approach on Gaussian random fields.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"105 ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41274860","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}
引用次数: 1
Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos 随机Lipschitz-Killing曲率:约简原理，分部积分和Wiener混沌
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-08-03 DOI: 10.1090/tpms/1170
Anna Vidotto
{"title":"Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos","authors":"Anna Vidotto","doi":"10.1090/tpms/1170","DOIUrl":"https://doi.org/10.1090/tpms/1170","url":null,"abstract":"In this survey we collect some recent results regarding the Lipschitz–Killing curvatures (LKCs) of the excursion sets of random eigenfunctions on the two-dimensional standard flat torus (arithmetic random waves) and on the two-dimensional unit sphere (random spherical harmonics). In particular, the aim of the present survey is to highlight the key role of integration by parts formulae in order to have an extremely neat expression for the random LKCs. Indeed, the main tool to study local geometric functionals of random waves on manifold is to exploit their Wiener chaos decomposition and show that (often), in the so-called high-energy limit, a single chaotic component dominates their behavior. Moreover, reduction principles show that the dominant Wiener chaotic component of LKCs of random waves’ excursion sets at threshold level \u0000\u0000 \u0000 \u0000 u\u0000 ≠\u0000 0\u0000 \u0000 une 0\u0000 \u0000\u0000 is proportional to the integral of \u0000\u0000 \u0000 \u0000 \u0000 H\u0000 2\u0000 \u0000 (\u0000 f\u0000 )\u0000 \u0000 H_2(f)\u0000 \u0000\u0000, \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000 being the random field of interest and \u0000\u0000 \u0000 \u0000 H\u0000 2\u0000 \u0000 H_2\u0000 \u0000\u0000 the second Hermite polynomial. This will be shown via integration by parts formulae.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41660632","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}
引用次数: 2
On the correlation between critical points and critical values for random spherical harmonics 随机球谐波的临界点与临界值的相关性
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-07-31 DOI: 10.1090/tpms/1164
Valentina Cammarota, Anna Todino
{"title":"On the correlation between critical points and critical values for random spherical harmonics","authors":"Valentina Cammarota, Anna Todino","doi":"10.1090/tpms/1164","DOIUrl":"https://doi.org/10.1090/tpms/1164","url":null,"abstract":"We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval \u0000\u0000 \u0000 \u0000 I\u0000 ⊂\u0000 \u0000 R\u0000 \u0000 \u0000 I subset mathbb {R}\u0000 \u0000\u0000. We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random \u0000\u0000 \u0000 \u0000 L\u0000 2\u0000 \u0000 L^2\u0000 \u0000\u0000-norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46762967","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}
引用次数: 0
Parametric estimation for functional autoregressive processes on the sphere 球面上函数自回归过程的参数估计
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-07-19 DOI: 10.1090/tpms/1165
Alessia Caponera, C. Durastanti
{"title":"Parametric estimation for functional autoregressive processes on the sphere","authors":"Alessia Caponera, C. Durastanti","doi":"10.1090/tpms/1165","DOIUrl":"https://doi.org/10.1090/tpms/1165","url":null,"abstract":"The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as weak consistency and asymptotic normality.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49112399","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}
引用次数: 0
Fractional stochastic partial differential equation for random tangent fields on the sphere 球面上随机切线场的分数阶随机偏微分方程
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-07-08 DOI: 10.1090/tpms/1142
V. Anh, A. Olenko, Yu Guang Wang
{"title":"Fractional stochastic partial differential equation for random tangent fields on the sphere","authors":"V. Anh, A. Olenko, Yu Guang Wang","doi":"10.1090/tpms/1142","DOIUrl":"https://doi.org/10.1090/tpms/1142","url":null,"abstract":"This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the Lévy-type behaviour of the spatial solution, a fractional derivative in time to depict the intermittency of its temporal solution, and is driven by vector-valued fractional Brownian motion on the unit sphere to characterize its temporal long-range dependence. The solution to the SPDE is presented in the form of the Karhunen-Loève expansion in terms of vector spherical harmonics. Its covariance matrix function is established as a tensor field on the unit sphere that is an expansion of Legendre tensor kernels. The variance of the increments and approximations to the solutions are studied and convergence rates of the approximation errors are given. It is demonstrated how these convergence rates depend on the decay of the power spectrum and variances of the fractional Brownian motion.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47164807","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}
引用次数: 4
A test on mean-variance efficiency of the tangency portfolio in high-dimensional setting 高维环境下切线投资组合的均方差效率检验
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-06-16 DOI: 10.1090/TPMS/1136
Stanislas Muhinyuza
{"title":"A test on mean-variance efficiency of the tangency portfolio in high-dimensional setting","authors":"Stanislas Muhinyuza","doi":"10.1090/TPMS/1136","DOIUrl":"https://doi.org/10.1090/TPMS/1136","url":null,"abstract":"In this paper we derive the asymptotic distribution of the test of the efficiency of the tangency portfolio in high-dimensional settings, namely when both the portfolio dimension and the sample siz ...","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45020288","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}
引用次数: 2
A note on last-success-problem 关于last-success-problem的注释
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-06-16 DOI: 10.1090/TPMS/1139
J. M. G. Ribas
{"title":"A note on last-success-problem","authors":"J. M. G. Ribas","doi":"10.1090/TPMS/1139","DOIUrl":"https://doi.org/10.1090/TPMS/1139","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":"103 1","pages":"155-165"},"PeriodicalIF":0.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45259958","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}
引用次数: 2
Editorial 编辑
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-06-16 DOI: 10.1090/tpms/1140
Y. Mishura, L. Sakhno, A. Veretennikov
{"title":"Editorial","authors":"Y. Mishura, L. Sakhno, A. Veretennikov","doi":"10.1090/tpms/1140","DOIUrl":"https://doi.org/10.1090/tpms/1140","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45884285","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}
引用次数: 0
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