Theory of Probability and Mathematical Statistics最新文献

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"title":"Closed-form estimator for the matrix-variate Gamma distribution","authors":"Gustav Alfelt","doi":"10.1090/TPMS/1138","DOIUrl":"https://doi.org/10.1090/TPMS/1138","url":null,"abstract":"In this paper we present a novel closed-form estimator for the parameters of the matrixvariate gamma distribution. The estimator relies on the moments of a transformation of the observed matrices, and is compared to the maximum likelihood estimator (MLE) through a simulation study. The study reveals that the suggested estimator outperforms the MLE, in terms of estimation error, when the underlying scale matrix parameter is ill-conditioned or when the shape parameter is close to its lower bound. In addition, since the suggested estimator is closed-form, it does not require numerical optimization as the MLE does, thus needing shorter computation time and is furthermore not subject to start value sensitivity or convergence issues. Finally, using the proposed estimator as start value in the optimization procedure of the MLE is shown to substantially reduce computation time, in comparison to using arbitrary start values.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45223114","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 modeling the correlation as an additional parameter in random effects model","authors":"Rebecca Nalule Muhumuza, Olha Bodnar","doi":"10.1090/TPMS/1137","DOIUrl":"https://doi.org/10.1090/TPMS/1137","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43289468","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":"Asymptotic results for certain first-passage times and areas of renewal processes","authors":"C. Macci, B. Pacchiarotti","doi":"10.1090/tpms/1189","DOIUrl":"https://doi.org/10.1090/tpms/1189","url":null,"abstract":"<p>We consider the process <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartSet x minus upper N left-parenthesis t right-parenthesis colon t greater-than-or-equal-to 0 EndSet\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mi>x</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>t</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>0</mml:mn> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{x-N(t):tgeq 0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x element-of double-struck upper R Subscript plus\"> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msub> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">xin mathbb {R}_+</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartSet upper N left-parenthesis t right-parenthesis colon t greater-than-or-equal-to 0 EndSet\"> <mml:semantics> <mml:mrow> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>t</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>0</mml:mn> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{N(t):tgeq 0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis tau left-parenthesis x right-parenthesis comma upper A left-parenthesis x right-parenthesis right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>τ<!-- τ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"f","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49188078","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}