Pub Date : 2025-12-19DOI: 10.1016/j.spl.2025.110629
Badr Elmansouri , Mohamed Marzougue
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.
{"title":"Generalized reflected backward doubly SDEs with irregular barriers and continuous coefficients","authors":"Badr Elmansouri , 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":"2025-12-19","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}
Pub Date : 2025-12-19DOI: 10.1016/j.spl.2025.110628
Minhan Wen , Ruoning Guan , Hui Jiang
In this paper, we consider the asymptotic properties of the maximum likelihood estimator of the drift coefficient in the Rayleigh diffusion process. Via the parameter-dependent change of measure method and precise asymptotic analysis techniques, we obtain the optimal Cramér-type moderate deviations and uniform Berry–Esseen bound.
{"title":"Berry–Esseen bound and Cramér-type moderate deviations of the maximum likelihood estimator in Rayleigh diffusion process","authors":"Minhan Wen , Ruoning Guan , Hui Jiang","doi":"10.1016/j.spl.2025.110628","DOIUrl":"10.1016/j.spl.2025.110628","url":null,"abstract":"<div><div>In this paper, we consider the asymptotic properties of the maximum likelihood estimator of the drift coefficient in the Rayleigh diffusion process. Via the parameter-dependent change of measure method and precise asymptotic analysis techniques, we obtain the optimal Cramér-type moderate deviations and uniform Berry–Esseen bound.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110628"},"PeriodicalIF":0.7,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841475","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}
Pub Date : 2025-12-18DOI: 10.1016/j.spl.2025.110627
Pier Giovanni Bissiri, Matteo Borrotti
Generative models for classification are a well-established method in statistics and machine learning. Martingales posteriors provide a computationally feasible method for performing prior-free Bayesian analysis. This paper aims to address the problem of uncertainty quantification through martingale posteriors for generative models for classification. To this aim, a conditionally identically distributed sequence of observations is considered. An empirical analysis is given.
{"title":"Martingale posteriors for generative classifiers","authors":"Pier Giovanni Bissiri, Matteo Borrotti","doi":"10.1016/j.spl.2025.110627","DOIUrl":"10.1016/j.spl.2025.110627","url":null,"abstract":"<div><div>Generative models for classification are a well-established method in statistics and machine learning. Martingales posteriors provide a computationally feasible method for performing prior-free Bayesian analysis. This paper aims to address the problem of uncertainty quantification through martingale posteriors for generative models for classification. To this aim, a conditionally identically distributed sequence of observations is considered. An empirical analysis is given.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110627"},"PeriodicalIF":0.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792040","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}
Pub Date : 2025-12-18DOI: 10.1016/j.spl.2025.110625
Shengli Zhao, Min Han, Zhaohui Yan
This paper introduces the -pattern, which is used to rank the columns of a baseline design, and proposes the minimum individual aberration (MIA) criterion for selecting baseline designs. We present an algorithm for completely searching MIA baseline designs using two-level orthogonal arrays. MIA baseline designs with run sizes of 8, 12, 16, and 20 are tabulated. Finally, we propose a partial order to rank the columns of a baseline design by their confounding severity.
{"title":"Minimum individual aberration two-level baseline designs","authors":"Shengli Zhao, Min Han, Zhaohui Yan","doi":"10.1016/j.spl.2025.110625","DOIUrl":"10.1016/j.spl.2025.110625","url":null,"abstract":"<div><div>This paper introduces the <span><math><mi>δ</mi></math></span>-pattern, which is used to rank the columns of a baseline design, and proposes the minimum individual aberration (MIA) criterion for selecting baseline designs. We present an algorithm for completely searching MIA baseline designs using two-level orthogonal arrays. MIA baseline designs with run sizes of 8, 12, 16, and 20 are tabulated. Finally, we propose a partial order to rank the columns of a baseline design by their confounding severity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110625"},"PeriodicalIF":0.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792041","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}
Pub Date : 2025-12-17DOI: 10.1016/j.spl.2025.110624
Sayantan Maitra , Aritra Mandal
The framework of Lie algebra has recently been proposed for establishing duals of various Markov processes. We apply this technique to obtain the dual processes of the Feller diffusion and the infinite dimensional interacting Wright-Fisher diffusion.
{"title":"Lie algebraic duality for some Markov processes","authors":"Sayantan Maitra , Aritra Mandal","doi":"10.1016/j.spl.2025.110624","DOIUrl":"10.1016/j.spl.2025.110624","url":null,"abstract":"<div><div>The framework of Lie algebra has recently been proposed for establishing duals of various Markov processes. We apply this technique to obtain the dual processes of the Feller diffusion and the infinite dimensional interacting Wright-Fisher diffusion.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110624"},"PeriodicalIF":0.7,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792039","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}
Pub Date : 2025-12-15DOI: 10.1016/j.spl.2025.110622
Lorenzo Camponovo
We study the relationship between stochastic and deterministic polynomial trends over the long-run, as the sample size , and at a local level, by focusing on the last observations of the sample, with . First, we show that stochastic processes with integration order , for integer , locally behave like deterministic polynomial trend models of degree , 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 , while Money Stock and Bond Yields exhibit , highlighting the effectiveness of our approach in detecting higher-order integration.
{"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":"2025-12-15","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}
Pub Date : 2025-12-14DOI: 10.1016/j.spl.2025.110623
Weiwei Zhuang, Yuting Su, Taizhong Hu
Negative dependence emerges through conditioning. In this paper, we establish sufficient conditions for a random vector to exhibit negative regression dependence, negative left-tail dependence and/or negative right-tail dependence when conditioned on the event that its component sum equals a constant or falls within a specified interval. Counterexamples are presented to delineate the conceptual distinctions among some notions of negative dependence.
{"title":"Generating negative regression dependence via conditioning operations","authors":"Weiwei Zhuang, Yuting Su, Taizhong Hu","doi":"10.1016/j.spl.2025.110623","DOIUrl":"10.1016/j.spl.2025.110623","url":null,"abstract":"<div><div>Negative dependence emerges through conditioning. In this paper, we establish sufficient conditions for a random vector to exhibit negative regression dependence, negative left-tail dependence and/or negative right-tail dependence when conditioned on the event that its component sum equals a constant or falls within a specified interval. Counterexamples are presented to delineate the conceptual distinctions among some notions of negative dependence.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110623"},"PeriodicalIF":0.7,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792042","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}
Pub Date : 2025-12-11DOI: 10.1016/j.spl.2025.110621
Lisa Parveen
Various properties of the ordering notion, namely decreasing in mean time to failure (DMTTF) order has been explored. Connections between DMTTF order and other well-known partial orderings of life distributions are established. Interrelationships with certain variability orderings are also explored. The applicability of the results has been demonstrated in the context of coherent systems with dependent but identically distributed components.
{"title":"On some properties of a partial ordering based on the mean time to failure function","authors":"Lisa Parveen","doi":"10.1016/j.spl.2025.110621","DOIUrl":"10.1016/j.spl.2025.110621","url":null,"abstract":"<div><div>Various properties of the ordering notion, namely decreasing in mean time to failure (DMTTF) order has been explored. Connections between DMTTF order and other well-known partial orderings of life distributions are established. Interrelationships with certain variability orderings are also explored. The applicability of the results has been demonstrated in the context of coherent systems with dependent but identically distributed components.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110621"},"PeriodicalIF":0.7,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786940","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}
Pub Date : 2025-12-06DOI: 10.1016/j.spl.2025.110619
Xuekang Zhang, Sijia Qiao
In this paper, we study the parameter estimation for non-stationary -stable Ornstein–Uhlenbeck processes with constant drift based on continuous observations. The consistency and limiting distributions for the estimators are obtained by integration by parts, the strong law of large numbers and the inner clock property for the -stable stochastic integral.
{"title":"Parameter estimation for non-stationary α-stable Ornstein–Uhlenbeck processes with constant drift","authors":"Xuekang Zhang, Sijia Qiao","doi":"10.1016/j.spl.2025.110619","DOIUrl":"10.1016/j.spl.2025.110619","url":null,"abstract":"<div><div>In this paper, we study the parameter estimation for non-stationary <span><math><mi>α</mi></math></span>-stable Ornstein–Uhlenbeck processes with constant drift based on continuous observations. The consistency and limiting distributions for the estimators are obtained by integration by parts, the strong law of large numbers and the inner clock property for the <span><math><mi>α</mi></math></span>-stable stochastic integral.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110619"},"PeriodicalIF":0.7,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738797","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}
Pub Date : 2025-12-06DOI: 10.1016/j.spl.2025.110620
Yanhui Jiao , Yanpeng Li
This note establishes the log-convexity of the sequence of th moments of averages of i.i.d. Gamma random variables for by using the properties of the Gamma function. Moreover, for integral , the log-convexity for the sequence of Poisson distribution is also demonstrated.
{"title":"Log-convexity of moments of averages of i.i.d. Gamma and Poisson random variables","authors":"Yanhui Jiao , Yanpeng Li","doi":"10.1016/j.spl.2025.110620","DOIUrl":"10.1016/j.spl.2025.110620","url":null,"abstract":"<div><div>This note establishes the log-convexity of the sequence of <span><math><mi>p</mi></math></span>th moments of averages of i.i.d. Gamma random variables for <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span> by using the properties of the Gamma function. Moreover, for integral <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, the log-convexity for the sequence of Poisson distribution is also demonstrated.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110620"},"PeriodicalIF":0.7,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705792","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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