{"title":"Transportation cost-information inequality for stochastic wave equation with spatially inhomogeneous white noise","authors":"Zhigang Yao, Bin Zhang, Junfeng Liu","doi":"10.1016/j.spl.2024.110321","DOIUrl":"10.1016/j.spl.2024.110321","url":null,"abstract":"<div><div>In this paper, we prove the existence, uniqueness and Hölder continuity of the mild solution to the nonlinear stochastic wave equation driven by spatially inhomogeneous white noise. Furthermore, we establish a Talagrand’s <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> transportation cost-information inequality for the law of the solution on the continuous path space with respect to the weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-metric.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110321"},"PeriodicalIF":0.9,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161025","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":"Stable approximation for call function via Stein’s method","authors":"Peng Chen , Tianyi Qi , Ting Zhang","doi":"10.1016/j.spl.2024.110328","DOIUrl":"10.1016/j.spl.2024.110328","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be a sum of independent identically distribution random variables with finite first moment and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> be a call function defined by <span><math><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>M</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>M</mi><mo>,</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> for <span><math><mrow><mi>x</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, <span><math><mrow><mi>M</mi><mo>></mo><mn>0</mn></mrow></math></span>. In this paper, we assume the random variables are in the domain <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> of normal attraction of a stable law of exponent <span><math><mi>α</mi></math></span>, then for <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>, we use the Stein’s method developed in Chen et al. (2024) to give uniform and non uniform bounds on <span><math><mi>α</mi></math></span>-stable approximation for the call function without additional moment assumptions. These results will make the approximation theory of call function applicable to the lower moment conditions, and greatly expand the scope of application of call function in many fields.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110328"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162100","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":"Limiting distribution for infinite-server batch service queues","authors":"Bara Kim , Jeongsim Kim","doi":"10.1016/j.spl.2024.110327","DOIUrl":"10.1016/j.spl.2024.110327","url":null,"abstract":"<div><div>Nakamura and Phung-Duc (2023) conjectured that, for an infinite-server batch service queue with Poisson arrivals, the central limit theorem for the number of busy servers, conditioned on the number of waiting customers and the size of the batch to be served, holds as the arrival rate goes to infinity. In this paper, we resolve this conjecture using the theory of Markov regenerative processes and further extend the result to renewal arrival models.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110327"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162101","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":"Kac’s central limit theorem by Stein’s method","authors":"Suprio Bhar , Ritwik Mukherjee , Prathmesh Patil","doi":"10.1016/j.spl.2024.110329","DOIUrl":"10.1016/j.spl.2024.110329","url":null,"abstract":"<div><div>In 1946, Mark Kac proved a Central Limit type theorem for a sequence of random variables that were not independent. The random variables under consideration were obtained from the angle-doubling map. The idea behind Kac’s proof was to show that although the random variables under consideration were not independent, they were what he calls <em>statistically independent</em> (in modern terminology, this concept is called long range independence). Using that observation, Kac showed that the sample averages of the random variables, suitably normalized, converges to the standard normal distribution. In this paper, we give a new proof of Kac’s result by applying Stein’s method. We show that the normalized sample averages converge to the standard normal distribution in the Wasserstein metric, which in particular implies convergence in distribution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110329"},"PeriodicalIF":0.9,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162103","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":"Almost sure convergence of the waiting time for a G/G/1 queue in heavy traffic","authors":"Ye Xia","doi":"10.1016/j.spl.2024.110326","DOIUrl":"10.1016/j.spl.2024.110326","url":null,"abstract":"<div><div>Consider a G/G/1 queueing model with traffic intensity <span><math><mrow><mi>ρ</mi><mo>=</mo><mn>1</mn></mrow></math></span>. Let <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be the waiting time in the queue for customer <span><math><mi>n</mi></math></span>. We provide a class of sufficient conditions for almost sure convergence of <span><math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> to 0, where <span><math><mrow><mi>α</mi><mo>></mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110326"},"PeriodicalIF":0.9,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162104","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 maximal correlation coefficient for the bivariate Marshall Olkin distribution","authors":"Axel Bücher, Torben Staud","doi":"10.1016/j.spl.2024.110323","DOIUrl":"10.1016/j.spl.2024.110323","url":null,"abstract":"<div><div>We prove a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution that was conjectured in Lin et al., 2016. The formula is applied to obtain a new proof for a variance inequality in extreme value statistics that links the disjoint and the sliding block maxima method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110323"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometric quantile-based measures of multivariate distributional characteristics","authors":"Ha-Young Shin, Hee-Seok Oh","doi":"10.1016/j.spl.2024.110325","DOIUrl":"10.1016/j.spl.2024.110325","url":null,"abstract":"<div><div>Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes, and are easy to calculate. Some theoretical justification is given, followed by experiments illustrating that they are sensible measures of these distributional characteristics and some basic empirical justification for bootstrapped confidence regions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110325"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162106","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":"Moderate deviations for the number of descents in a random permutation","authors":"Hui Jiang, Jing Wang","doi":"10.1016/j.spl.2024.110320","DOIUrl":"10.1016/j.spl.2024.110320","url":null,"abstract":"<div><div>The number of descents in a random permutation has close connections with generalized Pólya urn and random trees. Via the Laplace functional calculations and asymptotic analysis techniques, we prove that the number of descents satisfies the moderate deviations and Cramér type moderate deviations. Then, using the martingale difference representation, we establish the functional moderate deviations in <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> equipped with the uniform topology.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110320"},"PeriodicalIF":0.9,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162105","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":"New proofs to measurable, predictable and optional section theorems","authors":"Stefanos Theodorakopoulos","doi":"10.1016/j.spl.2024.110324","DOIUrl":"10.1016/j.spl.2024.110324","url":null,"abstract":"<div><div>We present new, short and elementary proofs of the famous section theorems that are used in Stochastic Calculus. Predictable section is proved directly while measurable section is a simple corollary. Then, optional (resp. accessible) section follows from an intuitive approximation argument based on the dichotomy of predictable and total inaccessible times.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110324"},"PeriodicalIF":0.9,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162108","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":"The first exit time of fractional Brownian motion from an unbounded domain","authors":"Yinbing Zhou, Dawei Lu","doi":"10.1016/j.spl.2024.110319","DOIUrl":"10.1016/j.spl.2024.110319","url":null,"abstract":"<div><div>Consider a fractional Brownian motions starting at the interior point <span><math><mrow><mfenced><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mi>h</mi><mfenced><mrow><mo>‖</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow></mfenced><mo>+</mo><mn>2</mn><mi>K</mi></mrow></mfenced><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></math></span> with the constant <span><math><mrow><mi>K</mi><mo>></mo><mn>1</mn></mrow></math></span>, for some fixed <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, of an unbounded domain <span><math><mrow><mi>D</mi><mo>=</mo><mfenced><mrow><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>:</mo><mi>y</mi><mo>></mo><mi>h</mi><mfenced><mrow><mo>‖</mo><mi>x</mi><mo>‖</mo></mrow></mfenced></mrow></mfenced></mrow></math></span>, The function <span><math><mi>h</mi></math></span> is a nondecreasing, lower semicontinuous, and convex function on <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> with <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> being finite. Here we take <span><math><mrow><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mfenced><mrow><mi>x</mi></mrow></mfenced><mo>=</mo><mi>A</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>α</mi></mrow></msup><msup><mrow><mfenced><mrow><mo>log</mo><mi>x</mi></mrow></mfenced></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span>with a positive constant <span><math><mi>A</mi></math></span> for <span><math><mrow><mi>x</mi><mo>></mo><mi>K</mi></mrow></math></span>. It is evident that <span><math><mrow><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> exhibits monotonic behavior for sufficiently large values of <span><math><mi>x</mi></math></span>. Let <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> denote the first time that the fractional Brownian motion exits from <span><math><mi>D</mi></math></span>. In most cases, we give the asymptotically equivalent estimate of <span><math><mrow><mo>log</mo><mi>P</mi><mfenced><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>></mo><mi>t</mi></mrow></mfenced></mrow></math></span>. The proof methods are based on the earlier works of Li, Shi, Lifshits, and Aurzada.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"218 ","pages":"Article 110319"},"PeriodicalIF":0.9,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149205","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}
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