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Probability solution for time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measure
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-12 DOI: 10.1016/j.spl.2025.110427
Siyan Xu , Huiyan Zhao
{"title":"Probability solution for time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measure","authors":"Siyan Xu ,&nbsp;Huiyan Zhao","doi":"10.1016/j.spl.2025.110427","DOIUrl":"10.1016/j.spl.2025.110427","url":null,"abstract":"<div><div>In this paper, we consider a class of generalized time-fractional Fokker–Planck–Kolmogorov equations with time–space-dependent Lévy measures, where time–space-dependent Lévy measures contain stable-like Lévy measures as special examples. After that, probability solutions are constructed for such Fokker–Planck–Kolmogorov equations based on the correspondence between the time–space-dependent Lévy measure and its related SDE.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110427"},"PeriodicalIF":0.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826482","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
Mean-field forward–backward stochastic differential equations driven by G-Brownian motion
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-12 DOI: 10.1016/j.spl.2025.110429
Shengqiu Sun
{"title":"Mean-field forward–backward stochastic differential equations driven by G-Brownian motion","authors":"Shengqiu Sun","doi":"10.1016/j.spl.2025.110429","DOIUrl":"10.1016/j.spl.2025.110429","url":null,"abstract":"<div><div>In this paper, we consider the mean-field forward–backward stochastic differential equations driven by <span><math><mi>G</mi></math></span>-Brownian motion with Lipschitz coefficients. The existence and uniqueness of solution on small time duration can be obtained by contraction mapping principle and some a prior estimates.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110429"},"PeriodicalIF":0.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829256","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
Comparison results of range-based quantities in the classical risk models
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-11 DOI: 10.1016/j.spl.2025.110428
Mohamed Amine Lkabous, Mengni Yang
{"title":"Comparison results of range-based quantities in the classical risk models","authors":"Mohamed Amine Lkabous,&nbsp;Mengni Yang","doi":"10.1016/j.spl.2025.110428","DOIUrl":"10.1016/j.spl.2025.110428","url":null,"abstract":"<div><div>In this paper, we investigate the range-based risk quantities in classical risk models. Specifically, we present some comparison results with respect to the stochastic ordering. We also propose some range-based VaR-type risk measures and study their properties, providing insights into their practical applications and implications for risk management.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110428"},"PeriodicalIF":0.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844100","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
Large sample properties of modified maximum likelihood estimator of the location parameter using moving extremes ranked set sampling
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-11 DOI: 10.1016/j.spl.2025.110430
Han Wang, Wangxue Chen
{"title":"Large sample properties of modified maximum likelihood estimator of the location parameter using moving extremes ranked set sampling","authors":"Han Wang,&nbsp;Wangxue Chen","doi":"10.1016/j.spl.2025.110430","DOIUrl":"10.1016/j.spl.2025.110430","url":null,"abstract":"<div><div>The maximum likelihood estimator (MLE) obtained using moving extremes ranked set sampling (MERSS) typically does not have a closed form expression. In this study, we investigate a modified MLE (MMLE) utilizing MERSS for estimating the location parameter of a location family and analyze its properties in large samples. We derive the explicit form of the MMLE for two common distributions when MERSS is employed. The numerical results from two usual distributions indicate that the MMLE using MERSS is more efficient than that the MLE using simple random sampling with an equivalent sample size. The numerical results also indicate the loss of efficiency in using the MMLE under MERSS instead of the MLE under MERSS is very small for small values of <span><math><mi>m</mi></math></span>. Additionally, we examine the implications of imperfect ranking and demonstrate our approach using a real dataset.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110430"},"PeriodicalIF":0.9,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834793","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 note on the maximum probability of ultra log-concave distributions
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-10 DOI: 10.1016/j.spl.2025.110418
Heshan Aravinda
{"title":"A note on the maximum probability of ultra log-concave distributions","authors":"Heshan Aravinda","doi":"10.1016/j.spl.2025.110418","DOIUrl":"10.1016/j.spl.2025.110418","url":null,"abstract":"<div><div>Jakimiuk et al. (2024) have proved that, if <span><math><mi>X</mi></math></span> is an ultra log-concave random variable with integral mean, then <span><math><mrow><munder><mrow><mo>max</mo></mrow><mrow><mi>n</mi></mrow></munder><mi>P</mi><mrow><mo>{</mo><mi>X</mi><mo>=</mo><mi>n</mi><mo>}</mo></mrow><mo>≥</mo><munder><mrow><mo>max</mo></mrow><mrow><mi>n</mi></mrow></munder><mi>P</mi><mrow><mo>{</mo><mi>Z</mi><mo>=</mo><mi>n</mi><mo>}</mo></mrow><mo>,</mo><mspace></mspace></mrow></math></span> where <span><math><mi>Z</mi></math></span> is a Poisson random variable with the parameter <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow></mrow></math></span>. In this note, we show that this inequality does not always hold true when <span><math><mi>X</mi></math></span> is ultra log-concave with <span><math><mrow><mi>E</mi><mrow><mo>[</mo><mi>X</mi><mo>]</mo></mrow><mo>&gt;</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110418"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823885","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
Mean reflected backward stochastic differential equations with jumps in a convex domain
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-10 DOI: 10.1016/j.spl.2025.110426
Hongchao Qian
{"title":"Mean reflected backward stochastic differential equations with jumps in a convex domain","authors":"Hongchao Qian","doi":"10.1016/j.spl.2025.110426","DOIUrl":"10.1016/j.spl.2025.110426","url":null,"abstract":"<div><div>In this paper, we study a class of multi-dimensional mean reflected backward stochastic differential equations driven by a Brownian motion and an independent Poisson random measure. In our setting, the constraint depends on the law of the solution rather than on its paths. Specifically, the expectation of the solution takes values in a convex domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The existence and uniqueness of solutions are established by a penalization method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110426"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815702","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
Lp-solutions of backward stochastic differential equations with default time
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-09 DOI: 10.1016/j.spl.2025.110407
Badr Elmansouri , Mohamed Marzougue
{"title":"Lp-solutions of backward stochastic differential equations with default time","authors":"Badr Elmansouri ,&nbsp;Mohamed Marzougue","doi":"10.1016/j.spl.2025.110407","DOIUrl":"10.1016/j.spl.2025.110407","url":null,"abstract":"<div><div>In this paper, we address the problem of existence and uniqueness of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-solutions for backward stochastic differential equations (BSDEs) with default time, for <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. Under appropriate <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-integrability conditions on the data and a <span><math><mi>γ</mi></math></span>-Lipschitz condition on the coefficient, where <span><math><mi>γ</mi></math></span> is the intensity process of the martingale associated with the default jump, we prove the existence and uniqueness of an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110407"},"PeriodicalIF":0.9,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815701","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
Lower bounds for density estimation on symmetric spaces
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-31 DOI: 10.1016/j.spl.2025.110416
Dena Marie Asta
{"title":"Lower bounds for density estimation on symmetric spaces","authors":"Dena Marie Asta","doi":"10.1016/j.spl.2025.110416","DOIUrl":"10.1016/j.spl.2025.110416","url":null,"abstract":"<div><div>We prove that kernel density estimation on symmetric spaces of non-compact type, whose <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110416"},"PeriodicalIF":0.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759730","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
Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110415
Min Hua , Gyuhyeong Goh
{"title":"Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors","authors":"Min Hua ,&nbsp;Gyuhyeong Goh","doi":"10.1016/j.spl.2025.110415","DOIUrl":"10.1016/j.spl.2025.110415","url":null,"abstract":"<div><div>In the context of Bayesian regression modeling, posterior model consistency provides frequentist validation for Bayesian variable selection. A question that has long been open is whether posterior model consistency holds under arbitrary priors when high-dimensional variable selection is performed. In this paper, we aim to give an answer by establishing sufficient conditions for priors under which the posterior model distribution converges to a degenerate distribution at the true model. Our framework considers high-dimensional regression settings where the number of potential predictors grows at a rate faster than the sample size. We demonstrate that a wide selection of priors satisfy the conditions that we establish in this paper.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110415"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734875","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 impact of contamination and correlated design on the Lasso: An average case analysis
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110417
Stanislav Minsker , Yiqiu Shen
{"title":"The impact of contamination and correlated design on the Lasso: An average case analysis","authors":"Stanislav Minsker ,&nbsp;Yiqiu Shen","doi":"10.1016/j.spl.2025.110417","DOIUrl":"10.1016/j.spl.2025.110417","url":null,"abstract":"<div><div>We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110417"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759731","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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