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Mean-field fractional BSDEs with locally monotone coefficients
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-30 DOI: 10.1016/j.spl.2025.110361
Zongkui Fu , Dandan Fei
{"title":"Mean-field fractional BSDEs with locally monotone coefficients","authors":"Zongkui Fu ,&nbsp;Dandan Fei","doi":"10.1016/j.spl.2025.110361","DOIUrl":"10.1016/j.spl.2025.110361","url":null,"abstract":"<div><div>In this paper, we study mean-field backward stochastic differential equations (BSDEs) driven by fractional Brownian motion with Hurst parameter <span><math><mi>H</mi></math></span> greater than <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>. With the help of choosing the suitable approximation sequence, we obtain the existence and uniqueness of solution to mean-field fractional BSDEs with locally monotone coefficients.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110361"},"PeriodicalIF":0.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095414","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}
引用次数: 0
Poisson approximation and D(un) condition for extremes of transient random walks in random sceneries
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-29 DOI: 10.1016/j.spl.2025.110364
Nicolas Chenavier, Ahmad Darwiche
{"title":"Poisson approximation and D(un) condition for extremes of transient random walks in random sceneries","authors":"Nicolas Chenavier,&nbsp;Ahmad Darwiche","doi":"10.1016/j.spl.2025.110364","DOIUrl":"10.1016/j.spl.2025.110364","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> be a transient random walk in the domain of attraction of a stable law and let <span><math><msub><mrow><mrow><mo>(</mo><mi>ξ</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>∈</mo><mi>Z</mi></mrow></msub></math></span> be a sequence of random variables. Under suitable assumptions, we establish a Poisson approximation result for the point process of exceedances associated with <span><math><msub><mrow><mrow><mo>(</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> and demonstrate that it satisfies the <span><math><mrow><mi>D</mi><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> condition.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110364"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095413","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}
引用次数: 0
The asymptotic behaviors for branching α-stable process
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-29 DOI: 10.1016/j.spl.2025.110362
Nana Luan , Li Wang
{"title":"The asymptotic behaviors for branching α-stable process","authors":"Nana Luan ,&nbsp;Li Wang","doi":"10.1016/j.spl.2025.110362","DOIUrl":"10.1016/j.spl.2025.110362","url":null,"abstract":"<div><div>We consider a branching symmetric <span><math><mi>α</mi></math></span>-stable process in which random split takes place at rate <span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We obtain results concerning the long-term behavior of the number of particles surpassing <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>λ</mi><mi>t</mi></mrow></msup></math></span> at time <span><math><mi>t</mi></math></span> for <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. Additionally, we derive the almost sure asymptotic speed of the rightmost particle as a consequence.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110362"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095415","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}
引用次数: 0
Logarithmic scale asymptotics for random walks with Weibull-like upper tail distributions
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-28 DOI: 10.1016/j.spl.2025.110363
George Stoica , Deli Li
{"title":"Logarithmic scale asymptotics for random walks with Weibull-like upper tail distributions","authors":"George Stoica ,&nbsp;Deli Li","doi":"10.1016/j.spl.2025.110363","DOIUrl":"10.1016/j.spl.2025.110363","url":null,"abstract":"<div><div>We present new asymptotic results in logarithmic scale for random walks with Weibull-like upper tail distributions. The rate of convergence is essentially dictated by the stretched exponential part of the tail distribution therein.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110363"},"PeriodicalIF":0.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095412","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}
引用次数: 0
A simple consensus model for an increasing population of agents with i.i.d incoming opinions
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-25 DOI: 10.1016/j.spl.2024.110345
Ioannis Markou
{"title":"A simple consensus model for an increasing population of agents with i.i.d incoming opinions","authors":"Ioannis Markou","doi":"10.1016/j.spl.2024.110345","DOIUrl":"10.1016/j.spl.2024.110345","url":null,"abstract":"<div><div>In this short note we study what happens in a symmetric opinion model when we send the total interacting population <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> to infinity as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. We assume that new population enters the system with opinions that are i.i.d random vectors with finite mean and variance. We give sharp conditions on the rate of population growth that is required for convergence to a global consensus in opinions. More particularly, we show that if the total population increases at a rate <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>∼</mo><msup><mrow><mi>e</mi></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow></msup></mrow></math></span>, then <span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> is necessary and sufficient condition for convergence to the mean of incoming opinions, and the convergence is achieved at an algebraic rate.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"220 ","pages":"Article 110345"},"PeriodicalIF":0.9,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143095411","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}
引用次数: 0
Construction of mixed-level designs with minimum discrete discrepancy
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-21 DOI: 10.1016/j.spl.2025.110358
Liuping Hu , Kashinath Chatterjee , Jianhui Ning , Hong Qin
{"title":"Construction of mixed-level designs with minimum discrete discrepancy","authors":"Liuping Hu ,&nbsp;Kashinath Chatterjee ,&nbsp;Jianhui Ning ,&nbsp;Hong Qin","doi":"10.1016/j.spl.2025.110358","DOIUrl":"10.1016/j.spl.2025.110358","url":null,"abstract":"<div><div>Mixed-level designs are widely applicable in various practical fields. In this paper, we introduce new methods for constructing mixed-level designs with minimum discrete discrepancy. Utilizing the minimum discrete discrepancy aberration criterion, we establish a valuable analytical connection between the initial design and the resultant design, demonstrating that a high-quality initial design ensures the quality of the resultant design. Additionally, we derive general lower bounds for the discrete discrepancy, which serve as benchmarks for assessing the uniformity of mixed-level designs. Examples are provided to illustrate the effectiveness of our construction methods and the significance of the newly derived lower bounds.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110358"},"PeriodicalIF":0.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161085","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}
引用次数: 0
Estimation of the optimal treatment regimes with multiple treatments under proportional hazards model
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-17 DOI: 10.1016/j.spl.2025.110357
Yuexin Fang , Xiangyong Tan , Qian Li
{"title":"Estimation of the optimal treatment regimes with multiple treatments under proportional hazards model","authors":"Yuexin Fang ,&nbsp;Xiangyong Tan ,&nbsp;Qian Li","doi":"10.1016/j.spl.2025.110357","DOIUrl":"10.1016/j.spl.2025.110357","url":null,"abstract":"<div><div>We propose a novel proportional hazards model that include an unknown baseline covariate effect and the interaction between multiple treatments and covariates on censored survival data. Doubly robust estimating equations constructed by utilizing the A-learning methodology and time-dependent propensity score. The asymptotic properties of the proposed estimators are established under the correct specification of either the baseline effect model or the propensity score model. Extensive simulation studies, along with an application, demonstrate the efficacy of the proposed approach.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110357"},"PeriodicalIF":0.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161560","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}
引用次数: 0
Sylvester’s problem for random walks and bridges
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-12 DOI: 10.1016/j.spl.2024.110349
Hugo Panzo
{"title":"Sylvester’s problem for random walks and bridges","authors":"Hugo Panzo","doi":"10.1016/j.spl.2024.110349","DOIUrl":"10.1016/j.spl.2024.110349","url":null,"abstract":"<div><div>Consider a random walk in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> that starts at the origin and whose increment distribution assigns zero probability to any affine hyperplane. We solve Sylvester’s problem for these random walks by showing that the probability that any <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> consecutive steps of the walk are in convex position is equal to <span><math><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span>. The analogous result also holds for random bridges of length at least <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> whose joint increment distribution is exchangeable.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110349"},"PeriodicalIF":0.9,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161558","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}
引用次数: 0
Choice of the hypothesis matrix for using the Anova-type-statistic
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-11 DOI: 10.1016/j.spl.2025.110356
Paavo Sattler , Manuel Rosenbaum
{"title":"Choice of the hypothesis matrix for using the Anova-type-statistic","authors":"Paavo Sattler ,&nbsp;Manuel Rosenbaum","doi":"10.1016/j.spl.2025.110356","DOIUrl":"10.1016/j.spl.2025.110356","url":null,"abstract":"<div><div>Initially developed in <span><span>Brunner et al. (1997)</span></span>, the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors <span><math><mrow><mi>θ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>. Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> can be expressed by various hypothesis matrices <span><math><mrow><mi>H</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi><mo>×</mo><mi>d</mi></mrow></msup></mrow></math></span> and corresponding vectors <span><math><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-type-statistic, for each hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110356"},"PeriodicalIF":0.9,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161559","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}
引用次数: 0
Construction of asymmetric resolvable orthogonal arrays
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-01-09 DOI: 10.1016/j.spl.2025.110355
Xiao Lin, Shanqi Pang
{"title":"Construction of asymmetric resolvable orthogonal arrays","authors":"Xiao Lin,&nbsp;Shanqi Pang","doi":"10.1016/j.spl.2025.110355","DOIUrl":"10.1016/j.spl.2025.110355","url":null,"abstract":"<div><div>Asymmetric resolvable orthogonal arrays have received more and more attention in experimental design, computer experiments, multiple experiments, cross validation, stochastic optimization, and quantum information. However, there are extremely few constructions of asymmetric resolvable orthogonal arrays. This article generalizes the definition of asymmetric resolvable orthogonal arrays and presents some approaches for constructing such arrays.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110355"},"PeriodicalIF":0.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161523","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}
引用次数: 0
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