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Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay 一类具有时滞和预期项的广义FBSDE的求解及其在时变时滞控制问题中的应用
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-25 DOI: 10.1016/j.spl.2025.110414
Yuecai Han , Yuhang Li , Zheng Li
{"title":"Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay","authors":"Yuecai Han ,&nbsp;Yuhang Li ,&nbsp;Zheng Li","doi":"10.1016/j.spl.2025.110414","DOIUrl":"10.1016/j.spl.2025.110414","url":null,"abstract":"<div><div>In this paper, motivated by optimal control problem with time-varying delay, we study a type of generalized forward–backward stochastic differential equation. Both delay and anticipated terms appear in both forward equation and backward equation. The existence and uniqueness of the solution is obtained. As an application, the linear quadratic optimal control problem, where both state process and control process contain time-varying delay, is solved.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110414"},"PeriodicalIF":0.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705736","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 novel approach for estimating multi-attribute Gaussian copula graphical models 一种估计多属性高斯联结图模型的新方法
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110413
Lijie Li , Yang Yu , Wanfeng Liang , Feng Zou
{"title":"A novel approach for estimating multi-attribute Gaussian copula graphical models","authors":"Lijie Li ,&nbsp;Yang Yu ,&nbsp;Wanfeng Liang ,&nbsp;Feng Zou","doi":"10.1016/j.spl.2025.110413","DOIUrl":"10.1016/j.spl.2025.110413","url":null,"abstract":"<div><div>This paper considers estimating multi-attribute Gaussian copula graphical models where each node represents multivariate variables with rich meanings. A two-stage semiparametric method is proposed to achieve modeling flexibility and estimation robustness simultaneously by utilizing normal score transformation. We derive the consistency of the proposed estimator under the spectral norm, and establish the theoretical guarantees on sparsistency under some mild conditions. Simulation studies and a real data example are provided to demonstrate the empirical performance of the proposed method. We provide the complete code supporting this article at <span><span>https://github.com/JerryLi-Stat/Multi-attribute-GCGM</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110413"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683346","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
Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises 时空白噪声驱动下随机金兹堡-朗道方程的运输成本不等式
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110409
Beibei Zhang
{"title":"Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises","authors":"Beibei Zhang","doi":"10.1016/j.spl.2025.110409","DOIUrl":"10.1016/j.spl.2025.110409","url":null,"abstract":"<div><div>In this paper, we establish transportation cost inequalities for the solution of the stochastic complex Ginzburg–Landau equation driven by a space–time white noise on the spaces <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>. The proof is based on the estimates of the nonlinear term.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110409"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696877","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
The local long-time behaviour for continuous-time branching processes 连续时间分支过程的局部长时间行为
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110412
Liuyan Li , Junping Li
{"title":"The local long-time behaviour for continuous-time branching processes","authors":"Liuyan Li ,&nbsp;Junping Li","doi":"10.1016/j.spl.2025.110412","DOIUrl":"10.1016/j.spl.2025.110412","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> be a continuous-time branching process. There is a normalizing function <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> such that <span><math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></math></span> converges almost surely to a random variable. In this paper, we obtain a local limit theorem for <span><math><mrow><mo>{</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span>, which refers to the asymptotic behaviour of <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><munder><mrow><mo>lim</mo></mrow><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></munder><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>x</mi></mrow></math></span> and <span><math><mrow><mi>x</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. This expands the existing results of the discrete-time branching processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110412"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715864","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
Weak limits of standardized sums of independent geometrically distributed random variables 独立几何分布随机变量的标准化和的弱极限
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-23 DOI: 10.1016/j.spl.2025.110410
José A. Adell
{"title":"Weak limits of standardized sums of independent geometrically distributed random variables","authors":"José A. Adell","doi":"10.1016/j.spl.2025.110410","DOIUrl":"10.1016/j.spl.2025.110410","url":null,"abstract":"<div><div>We consider standardized sums of independent geometrically distributed random variables whose failure probabilities approach the unity. We show that such sums converge in law to a random variable having an infinitely divisible distribution whose characteristic function depends on the values of the Riemann zeta function at integer arguments. This is motivated by a probabilistic representation of the Stirling numbers of the second kind.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110410"},"PeriodicalIF":0.9,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704104","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
Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator 基于条件风险值的Pickands估计的渐近正态性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-21 DOI: 10.1016/j.spl.2025.110411
Yizhou Li , Paweł Polak
{"title":"Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator","authors":"Yizhou Li ,&nbsp;Paweł Polak","doi":"10.1016/j.spl.2025.110411","DOIUrl":"10.1016/j.spl.2025.110411","url":null,"abstract":"<div><div>We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110411"},"PeriodicalIF":0.9,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704048","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 designs with space-filling and orthogonal property 具有空间填充和正交特性的设计施工
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-19 DOI: 10.1016/j.spl.2025.110408
Min Li , Yuan Feng , Xiao Wang , Weiping Zhou
{"title":"Construction of designs with space-filling and orthogonal property","authors":"Min Li ,&nbsp;Yuan Feng ,&nbsp;Xiao Wang ,&nbsp;Weiping Zhou","doi":"10.1016/j.spl.2025.110408","DOIUrl":"10.1016/j.spl.2025.110408","url":null,"abstract":"<div><div>Space-filling designs are widely used in computer experiments, but their construction presents significant challenges. This paper introduces novel methods for generating maximin distance Latin hypercube designs (LHDs) and space-filling balanced designs with a slice structure, removing the reliance on computational searches. We also offer a simple yet effective approach to constructing sliced Latin hypercube designs (SLHDs), which achieve space-filling in each slice and maintain good orthogonality and stratification properties across the entire design. The resulting designs are more space-filling than existing designs.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110408"},"PeriodicalIF":0.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683335","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
Asymptotic optimality of generalized cross validation and regularized Mallows model averaging 广义交叉验证和正则化Mallows模型平均的渐近最优性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-15 DOI: 10.1016/j.spl.2025.110406
Chenchen Zou , Xin Li , Xinmin Li , Hua Liang
{"title":"Asymptotic optimality of generalized cross validation and regularized Mallows model averaging","authors":"Chenchen Zou ,&nbsp;Xin Li ,&nbsp;Xinmin Li ,&nbsp;Hua Liang","doi":"10.1016/j.spl.2025.110406","DOIUrl":"10.1016/j.spl.2025.110406","url":null,"abstract":"<div><div>We propose a modified generalized cross-validation model averaging procedure for weight choice and prove the asymptotic optimality of the resultant estimators in the squared loss sense under much weaker assumptions than those imposed in the literature. The proposed model averaging can be regarded as an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-regularized Mallows model averaging with varying coefficients. Furthermore, we propose a GCV-adjusted Mallows model averaging that achieves a faster convergence rate towards the optimal loss compared to using generalized cross-validation model averaging or Mallows model averaging individually. The performance of the proposed estimators is thoroughly evaluated through numerical experiments.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110406"},"PeriodicalIF":0.9,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636523","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
On the partial sums and extreme order statistics of i.i.d. random variables i.i.d随机变量的部分和和极序统计量
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-11 DOI: 10.1016/j.spl.2025.110405
Jiacheng Ye, Xin Chen, Jinghong Xiao
{"title":"On the partial sums and extreme order statistics of i.i.d. random variables","authors":"Jiacheng Ye,&nbsp;Xin Chen,&nbsp;Jinghong Xiao","doi":"10.1016/j.spl.2025.110405","DOIUrl":"10.1016/j.spl.2025.110405","url":null,"abstract":"<div><div>This paper proves several limit theorems for the joint version of partial sums and extreme order statistics. The obtained results extend those of Li et al. (2024) to the case where the random variables have infinite variances.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110405"},"PeriodicalIF":0.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636524","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
Strong convergence order for slow-fast SDEs in Hölder norm Hölder范数下慢速SDEs的强收敛阶
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-09 DOI: 10.1016/j.spl.2025.110398
Jicheng Liu, Guiling Long
{"title":"Strong convergence order for slow-fast SDEs in Hölder norm","authors":"Jicheng Liu,&nbsp;Guiling Long","doi":"10.1016/j.spl.2025.110398","DOIUrl":"10.1016/j.spl.2025.110398","url":null,"abstract":"<div><div>In this paper, we first derive a criterion for strong convergence in Hölder norm by the Garsia–Rodemich–Rumsey’s lemma. Then we apply the criterion to a class of stochastic differential equations with slow and fast time-scales, and deduce the averaging principle in Hölder norm using the technique of Poisson equation. As a byproduct, the strong convergence in sup-norm can be obtained.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110398"},"PeriodicalIF":0.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593021","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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