Statistics & Probability Letters最新文献

{"title":"Some general strong laws of large numbers for sequence of measurable operators","authors":"Nguyen Van Quang ,&nbsp;Ali Talebi","doi":"10.1016/j.spl.2025.110551","DOIUrl":"10.1016/j.spl.2025.110551","url":null,"abstract":"<div><div>In this paper, we establish some general laws of large numbers for sequence of measurable operators such that several known strong law of large numbers (LLN) in von Neumann algebras. One of our main achievements extends the main result of Jajte (2003) in some senses such that Batty’s strong LLN and Łuczak’s result are obtained as special cases. The result is new even in the case of classical random variables.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110551"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046176","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}

{"title":"Normal approximation for call function of m-dependent random variables with 2+δ-th moment","authors":"Ting Zhang ,&nbsp;Lulu Tian ,&nbsp;Tianyi Qi","doi":"10.1016/j.spl.2025.110550","DOIUrl":"10.1016/j.spl.2025.110550","url":null,"abstract":"<div><div>For the call function <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mi>x</mi><mo>−</mo><mi>k</mi><mo>,</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> with some fixed <span><math><mrow><mi>k</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, we apply Stein’s method to give the upper bounds of normal approximation under the weaker moment condition, containing both uniform and non uniform situations. Specifically, we discuss a sum of <span><math><mi>m</mi></math></span>-dependent and identically distributed random variables with weaker (<span><math><mrow><mn>2</mn><mo>+</mo><mi>δ</mi></mrow></math></span>)-th moment for some <span><math><mrow><mi>δ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Our results enable the application in call function to possess a broader field with normal approximation techniques.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110550"},"PeriodicalIF":0.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046178","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}

{"title":"Quasi-likelihood estimation for stochastic fractional heat equation","authors":"Yaqin Sun ,&nbsp;Jingqi Han ,&nbsp;Litan Yan","doi":"10.1016/j.spl.2025.110549","DOIUrl":"10.1016/j.spl.2025.110549","url":null,"abstract":"<div><div>By the quasi-likelihood method, in this note we consider parameter estimation of the fractional heat equation <span><span><span><math><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>t</mi><mo>+</mo><mi>σ</mi><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><mi>R</mi></mrow></math></span></span></span>with initial condition <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is a space–time white noise and <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>=</mo><mo>−</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span> is the fractional Laplacian with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span>. By using the quasi-likelihood method we obtain the estimator of <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and give the asymptotic behaviors of the estimator provided that the spatial process <span><math><mrow><mi>x</mi><mo>↦</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> can be observed at some discrete points <span><math><mrow><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>=</mo><mi>j</mi><mi>h</mi><mo>,</mo><mi>j</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></math></span> with <span><math><mrow><mi>h</mi><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>→</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>n</mi><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>γ</mi></mrow></msup><mo>→</mo><mi>R</mi><mo>≠</mo><mn>0</mn></mrow></math></span> for some <span><math><mrow><mn>0</mn><mo>≤</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, as <span><math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110549"},"PeriodicalIF":0.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060466","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}

{"title":"Dirichlet eigenvalue criteria for super Poincaré inequalities","authors":"Tao Wang","doi":"10.1016/j.spl.2025.110548","DOIUrl":"10.1016/j.spl.2025.110548","url":null,"abstract":"<div><div>In this paper, we present the criteria for super-Poincaré inequalities by using the first Dirichlet eigenvalues under some proper assumptions. Furthermore, I will illustrate the applicability of the result to a range of classic models, including jump processes, diffusion processes, and SDEs driven by symmetric stable processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110548"},"PeriodicalIF":0.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046177","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}

{"title":"Large deviations for a randomly indexed branching process with immigration","authors":"Zhenlong Gao","doi":"10.1016/j.spl.2025.110546","DOIUrl":"10.1016/j.spl.2025.110546","url":null,"abstract":"<div><div>Consider a supercritical continuous time branching process called randomly indexed branching processes with immigration. Large deviation results are established for the logarithms of such processes. Our results show that when the offspring distribution belongs to the Schröder case, the immigration distribution affects the rate function of the large deviation, while when the offspring distribution belongs to the Böttcher case, the immigration distribution has no effect on the rate function.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110546"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010249","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}

{"title":"Gaussian product inequalities for absolute raw moments","authors":"Haruhiko Ogasawara","doi":"10.1016/j.spl.2025.110552","DOIUrl":"10.1016/j.spl.2025.110552","url":null,"abstract":"<div><div>Gaussian product inequalities (GPIs) for absolute raw moments of real-valued orders are shown, where the orders include negative signs and mixed ones (positive and negative). The GPIs are for structural correlation matrices with a single parameter showing compound symmetric and autoregressive patterns with a non-zero common mean in each model. In the bivariate case, we have an extended so-called opposite GPI for the absolute raw moments. The GPIs are obtained by a known series formula of the Gaussian product absolute raw moments.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110552"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019574","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}

{"title":"Functional limit theorems for some self-similar Gaussian processes in critical and subcritical cases","authors":"Heguang Liu","doi":"10.1016/j.spl.2025.110547","DOIUrl":"10.1016/j.spl.2025.110547","url":null,"abstract":"<div><div>In this paper, under certain conditions, we investigate the asymptotic behavior of <span><math><mrow><mo>{</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>H</mi></mrow></msup><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>−</mo><mi>λ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mi>d</mi><mi>s</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span>, where <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> is the density of symmetric <span><math><mi>α</mi></math></span>-stable random variables with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>X</mi><mo>=</mo><mrow><mo>{</mo><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn></mrow><mo>}</mo></mrow></mrow></math></span> is some self-similar Gaussian process with index <span><math><mrow><mi>H</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. We mainly focus on the critical case <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mn>2</mn><mi>α</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span> and the subcritical case <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mn>2</mn><mi>α</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>&lt;</mo><mn>1</mn></mrow></math></span>. This work will extend the corresponding results in Hong et al. (2024) and may give another definition for the fractional derivative of local times of the Gaussian process <span><math><mi>X</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110547"},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026630","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}

{"title":"Palm versions of Hawkes processes","authors":"Matthias Kirchner","doi":"10.1016/j.spl.2025.110531","DOIUrl":"10.1016/j.spl.2025.110531","url":null,"abstract":"<div><div>This brief paper identifies the Palm distribution of a linear Hawkes process. The textbook example for Palm distributions is the Palm version of a stationary Poisson process that corresponds to the original process plus a point in zero. The present result generalizes this example in a more complex but nevertheless tractable way. As a next step, we derive the intensity measure of the Palm version of a Hawkes process and show how it could be used for estimation. Finally, we discuss further possible applications to the theory of Hawkes processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110531"},"PeriodicalIF":0.7,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917648","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}

{"title":"Approximate distribution of eigenvalues of a generalized Wishart matrix under an extended Gaussian model","authors":"Koki Shimizu,&nbsp;Hiroki Hashiguchi","doi":"10.1016/j.spl.2025.110535","DOIUrl":"10.1016/j.spl.2025.110535","url":null,"abstract":"<div><div>This paper discusses the distribution of the eigenvalues of a gamma matrix, which is generated from the product of an extended Gaussian matrix and its transposed matrix. We show that the distributions of the individual eigenvalues of a gamma matrix are approximated by the univariate gamma distribution when the first few eigenvalues of the scale parameter matrix are infinitely dispersed. Our results cover the eigenvalue distributions under the Gaussian and Kotz-type I models as special cases.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110535"},"PeriodicalIF":0.7,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921177","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}

{"title":"A practical flight-phase approach to balanced random sampling","authors":"Yves Tillé","doi":"10.1016/j.spl.2025.110536","DOIUrl":"10.1016/j.spl.2025.110536","url":null,"abstract":"<div><div>This paper introduces a straightforward method for selecting a balanced random sample from a population. The procedure involves a flight phase, which transforms the vector of inclusion probabilities into one with components close to 0 or 1, followed by a landing phase to complete the selection. We present a novel implementation of the flight phase that leverages linear programming, enabling a highly concise and easily interpretable R code. The method is formally described, implemented in R, and illustrated using real population data. This approach offers a practical, transparent, and reproducible solution to the balanced sampling problem, while establishing a direct link to linear programming techniques.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110536"},"PeriodicalIF":0.7,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892980","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}