Statistics & Probability Letters最新文献

{"title":"Synchronization of coupled system driven by additive fractional Brownian motion","authors":"Meiling Zhao","doi":"10.1016/j.spl.2026.110657","DOIUrl":"10.1016/j.spl.2026.110657","url":null,"abstract":"<div><div>This paper examines the synchronization of a stochastic coupled system driven by fractional Brownian motion with Hurst parameter <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>H</mi><mo>&lt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. A key aspect of our analysis is the study of the uniform boundedness of the fractional Ornstein–Uhlenbeck process with a singular parameter, which serves as a crucial tool in determining the convergence rate of synchronization.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110657"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023409","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":"Friedman vs Pólya","authors":"Raphael Alves ,&nbsp;Rafael A. Rosales","doi":"10.1016/j.spl.2025.110635","DOIUrl":"10.1016/j.spl.2025.110635","url":null,"abstract":"<div><div>Suppose an urn contains initially any number of balls of two colours. One ball is drawn randomly and then put back with <span><math><mi>α</mi></math></span> balls of the same colour and <span><math><mi>β</mi></math></span> balls of the opposite colour. Both cases, <span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are well known and correspond respectively to Pólya’s and Friedman’s replacement schemes. We consider a mixture of both of these: with probability <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> balls are replaced according to Friedman’s recipe and with probability <span><math><mrow><mn>1</mn><mo>−</mo><mi>p</mi></mrow></math></span> according to the one by Pólya. Independently of the initial urn composition and independently of <span><math><mi>α</mi></math></span>, <span><math><mi>β</mi></math></span>, and the value of <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, we show that the proportion of balls of one colour converges almost surely to <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>. The latter is the limit behaviour obtained by using Friedman’s scheme alone, i.e. when <span><math><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></math></span>. Our result follows by adapting an argument due to D. S. Ornstein.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110635"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886128","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":"Increasing and other subsequence problems for random interval sequences","authors":"İlker Arslan ,&nbsp;Ümi̇t Işlak","doi":"10.1016/j.spl.2026.110638","DOIUrl":"10.1016/j.spl.2026.110638","url":null,"abstract":"<div><div>Various relations for comparison of intervals of real numbers are introduced, and the expected length of the corresponding longest increasing subsequence is analyzed. When intervals are randomly generated by taking the minimum and maximum of two independent uniform random variables, we prove that the expected length of the longest increasing subsequence grows on the order of <span><math><mroot><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></mroot></math></span>. We also investigate the asymptotic behavior of the expected length under alternative comparison relations and random interval models. Discussions on other subsequence problems for interval sequences are included.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110638"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928319","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":"Moments of Hölder coefficients on random time intervals","authors":"Frank T. Seifried,&nbsp;Maximilian Würschmidt","doi":"10.1016/j.spl.2025.110634","DOIUrl":"10.1016/j.spl.2025.110634","url":null,"abstract":"<div><div>We show existence of moments for Hölder coefficients up to a random time. Our result applies to general processes satisfying Kolmogorov’s tightness criterion and (unbounded) random times with a higher moment. The proof is based on a ramification of Kolmogorov’s classical dyadic numbers argument. We illustrate the result for diffusions and BSDEs on unbounded time horizons.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110634"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972703","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":"Moment inequalities for a class of symmetric distributions","authors":"Weiwei Zhuang,&nbsp;Taizhong Hu","doi":"10.1016/j.spl.2026.110652","DOIUrl":"10.1016/j.spl.2026.110652","url":null,"abstract":"<div><div>For a class of symmetrically distributed random vectors <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></math></span> with finite mean, it is shown that <span><math><mrow><mi>E</mi><mrow><mo>|</mo><mi>X</mi><mo>+</mo><mi>Y</mi><mo>|</mo></mrow><mo>≥</mo><mi>E</mi><mrow><mo>|</mo><mi>X</mi><mo>−</mo><mi>Y</mi><mo>|</mo></mrow></mrow></math></span> holds, along with its generalizations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110652"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979442","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":"Stochastic stability for linear autoregressive model with Gaussian innovations","authors":"Ling-Di Wang ,&nbsp;Yu Chen ,&nbsp;Yong-Hua Mao ,&nbsp;Yu-Hui Zhang","doi":"10.1016/j.spl.2026.110656","DOIUrl":"10.1016/j.spl.2026.110656","url":null,"abstract":"<div><div>Autoregressive model is a basic one among those time series models, whose stochastic stability is crucial, and often a prerequisite, for statistical inference and other applications. As a specific type of time series model, the linear autoregressive model has garnered significant attention due to its simplicity and ease of generalization. In this paper, we present a comprehensive characterization of stability for the linear autoregressive model with Gaussian innovations, including recurrence and transience, the convergence rate in the ergodicity case, and R-stability in the transience case. The linear autoregressive models are fully classified according to their stability, which is entirely determined by their coefficients.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110656"},"PeriodicalIF":0.7,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023408","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 relationship between stochastic and deterministic polynomial trends with applications to the detection of the order of integration","authors":"Lorenzo Camponovo","doi":"10.1016/j.spl.2025.110622","DOIUrl":"10.1016/j.spl.2025.110622","url":null,"abstract":"<div><div>We study the relationship between stochastic and deterministic polynomial trends over the long-run, as the sample size <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, and at a local level, by focusing on the last <span><math><mi>n</mi></math></span> observations of the sample, with <span><math><mrow><mi>n</mi><mo>=</mo><mi>o</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>. First, we show that stochastic processes with integration order <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span>, for integer <span><math><mrow><mi>d</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, locally behave like deterministic polynomial trend models of degree <span><math><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></math></span>, scaled by asymptotically normal random variables that are constants at a local level. Second, we introduce statistical procedures to determine the order of polynomial trend models, thereby providing an indirect way to assess integration in stochastic processes. Using data on fourteen major U.S. macroeconomic variables, our method confirms that most are <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, while Money Stock and Bond Yields exhibit <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, highlighting the effectiveness of our approach in detecting higher-order integration.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110622"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792043","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":"An identity for the bias in Markov reward processes with applications to Markov chain perturbation and Kemeny’s constant","authors":"Ronald Ortner","doi":"10.1016/j.spl.2025.110592","DOIUrl":"10.1016/j.spl.2025.110592","url":null,"abstract":"<div><div>Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span>, which offers an intuitive explanation why it is a constant.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110592"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580287","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":"Generalized reflected backward doubly SDEs with irregular barriers and continuous coefficients","authors":"Badr Elmansouri ,&nbsp;Mohamed Marzougue","doi":"10.1016/j.spl.2025.110629","DOIUrl":"10.1016/j.spl.2025.110629","url":null,"abstract":"<div><div>In this note, we establish the existence of a minimal solution for a class of reflected generalized backward doubly stochastic differential equations with continuous and stochastic linear growth coefficients. The reflecting obstacle is not assumed to be right-continuous, but only right-upper semi-continuous and left-limited, and the noise is driven by two mutually independent Brownian motions and an independent integer-valued random measure. Our analysis begins with the case of stochastic Lipschitz coefficients, where we prove the existence and uniqueness results along with presenting a comparison result, which then allows us to derive the main existence finding of a minimal solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110629"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841455","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":"Central limit theorems for divergent higher-order Hermite integrals of Brownian motion","authors":"Yinmeng Chen ,&nbsp;Xiaoyu Xia ,&nbsp;Litan Yan","doi":"10.1016/j.spl.2025.110636","DOIUrl":"10.1016/j.spl.2025.110636","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>B</mi><mo>=</mo><mrow><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> be a standard Brownian motion. This paper establishes the asymptotic normality of renormalized Hermite integrals <span><math><mrow><msub><mrow><mi>Υ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo>≔</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><msubsup><mrow><mo>∫</mo></mrow><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mfrac><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><mi>s</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></msup></mrow></mfrac><mi>d</mi><mi>s</mi><mo>,</mo><mspace></mspace><mi>m</mi><mo>∈</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>…</mo><mo>}</mo></mrow><mo>,</mo></mrow></math></span> where <span><math><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>m</mi></mrow></msup><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>/</mo><msqrt><mrow><mi>y</mi></mrow></msqrt><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>y</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> denotes the classical Hermite polynomial of order <span><math><mi>m</mi></math></span>. We prove that as <span><math><mrow><mi>ɛ</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span>, <span><math><mrow><msub><mrow><mi>Υ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow><mo>⟶</mo><mi>N</mi><mfenced><mrow><mn>0</mn><mo>,</mo><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></mfenced><mo>,</mo><mspace></mspace><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><mn>2</mn><mspace></mspace><mi>m</mi><mo>)</mo></mrow><mo>!</mo></mrow><mrow><mrow><mo>(</mo><mn>2</mn><mi>m</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>m</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></mfrac><mo>,</mo></mrow></math></span> in distribution. This result quantifies the Gaussian limit behavior of divergent Hermite integrals through renormalization.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110636"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884651","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}