Statistics & Probability Letters最新文献

{"title":"The Borel–Cantelli lemma under m-dependence","authors":"Dawei Lu,&nbsp;Yunpeng Shi,&nbsp;Junhan Zhao","doi":"10.1016/j.spl.2025.110525","DOIUrl":"10.1016/j.spl.2025.110525","url":null,"abstract":"<div><div>Let <span><math><msubsup><mrow><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></math></span> be an <span><math><mi>m</mi></math></span>-dependent sequence of events. In this paper, we proved the second part of the Borel–Cantelli lemma still holds under <span><math><mi>m</mi></math></span>-dependence. Furthermore, we also obtained the quantitative version of this result.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110525"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860297","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":"2026-01-01","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":"Parameter estimation of Burgers equations driven by white-colored noise","authors":"Yiming Jiang ,&nbsp;Yujue Wang ,&nbsp;Jie Xue","doi":"10.1016/j.spl.2025.110553","DOIUrl":"10.1016/j.spl.2025.110553","url":null,"abstract":"<div><div>In this paper, we study the stochastic generalized Burgers equation driven by a white-colored noise with the <span><math><mi>α</mi></math></span>-order heat kernel. First we construct a parametric estimator of the drift parameter through temporal quadratic variation of the solution. Then we obtain the consistency and convergence rate of the estimator.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110553"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046179","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":"2026-01-01","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":"On the mean absorption time of multiple coalescing particles with removal at previously visited vertices","authors":"Mario A. Estrada ,&nbsp;Alex D. Ramos ,&nbsp;Pablo M. Rodriguez","doi":"10.1016/j.spl.2025.110523","DOIUrl":"10.1016/j.spl.2025.110523","url":null,"abstract":"<div><div>We study a stochastic process of multiple coalescing particles. In our process, <span><math><mi>k</mi></math></span> particles begin at an arbitrary but fixed vertex of a complete graph. Each particle performs an independent discrete-time symmetric random walk on the graph. When two or more particles meet at a given vertex, they merge into a single particle that continues the random walk through the graph. If a particle jumps to a vertex that has been previously visited by another particle, it is removed from the system. We analyze the asymptotic behavior of the absorption time of the process; i.e., the number of steps until the last particle is removed from the system.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110523"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860662","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":"Asymptotic behavior of finite-time ruin probabilities in a bidimensional compound risk model","authors":"Jinjin Zhang ,&nbsp;Yang Yang ,&nbsp;Lin Xu","doi":"10.1016/j.spl.2025.110529","DOIUrl":"10.1016/j.spl.2025.110529","url":null,"abstract":"<div><div>Consider a bidimensional compound risk model with stochastic premiums and returns, in which an insurer makes both risk-free and risky investments in two lines of business, and an accident may cause more than one claim. In this model, we allow that the two log-price processes are both real-valued Lévy processes, the claim numbers from the same business line, the two accident arrival processes and the two premium processes from two business lines are, respectively, arbitrarily dependent, and the premium processes are also arbitrarily dependent on all other random sources except the log-price processes. Under the condition that all claims from the same line are pairwise quasi-asymptotically independent and consistently varying-tailed, this paper establishes the asymptotic formulas for two types of finite-time ruin probabilities.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110529"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864936","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":"2026-01-01","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":"Transportation cost-information inequality for non-linear time-fractional stochastic heat equation driven by space–time white noise","authors":"Ruinan Li ,&nbsp;Yumeng Li","doi":"10.1016/j.spl.2025.110519","DOIUrl":"10.1016/j.spl.2025.110519","url":null,"abstract":"<div><div>We establish transportation cost-information inequalities <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>2</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></mrow></math></span> for solutions of nonlinear stochastic partial differential equation of fractional order in both space and time variables with deterministic and bounded initial conditions: <span><span><span><math><mrow><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><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><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mfenced><mrow><mi>σ</mi><mrow><mo>(</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></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></mfenced><mspace></mspace><mspace></mspace><mtext>in</mtext><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span>, <span><math><mrow><mi>γ</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><msubsup><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>β</mi></mrow></msubsup></math></span> is the Caputo fractional derivative, <span><math><mrow><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/power of Laplacian, <span><math><msubsup><mrow><mi>I</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></math></span> is the Riemann–Liouville integral operator, <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><mi>σ</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></mrow></math></span> is a bounded and Lipschitz function. Since the space variable is defined on the unbounded domain <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, the inequalities are proved under a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm in the spatial domain.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110519"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860660","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":"2026-01-01","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}

{"title":"A note on the geodesic normal distribution on the sphere","authors":"José E. Chacón ,&nbsp;Andrea Meilán-Vila","doi":"10.1016/j.spl.2025.110532","DOIUrl":"10.1016/j.spl.2025.110532","url":null,"abstract":"<div><div>This paper presents an alternative formulation of the geodesic normal distribution on the sphere, building on the work of <span><span>Hauberg (2018)</span></span>. While the isotropic version of this distribution is naturally defined on the sphere, the anisotropic version requires projecting points from the sphere onto the tangent space. In contrast, our approach removes the dependence on the tangent space and defines the geodesic normal distribution directly on the sphere. Moreover, we demonstrate that the density contours of this distribution are exactly ellipses on the sphere, providing intriguing alternative characterizations for describing this locus of points.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110532"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908721","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}