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Exact quantiles of Gaussian process extremes 高斯过程极值的精确定量
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-04 DOI: 10.1016/j.spl.2024.110173
Lijian Yang
{"title":"Exact quantiles of Gaussian process extremes","authors":"Lijian Yang","doi":"10.1016/j.spl.2024.110173","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110173","url":null,"abstract":"<div><p>Under nearly minimal conditions, continuity of extreme distribution function is established for both continuous Gaussian processes and finite Gaussian sequences, which entails existence of exact quantiles at any level. Also proved under simple conditions is strict monotonicity of extreme distribution functions that ensures uniqueness of exact quantiles at any level. These results provide convenient tools for developing statistical theory about global inference on functions.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141289146","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
Exponential ergodicity for reflected SDEs with interaction in a multidimensional general domain 多维一般域中具有交互作用的反射自变量的指数遍历性
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-04 DOI: 10.1016/j.spl.2024.110168
Ping Chen , Tusheng Zhang
{"title":"Exponential ergodicity for reflected SDEs with interaction in a multidimensional general domain","authors":"Ping Chen ,&nbsp;Tusheng Zhang","doi":"10.1016/j.spl.2024.110168","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110168","url":null,"abstract":"<div><p>In this paper, we consider reflected stochastic differential equations (SDEs) with interaction in a multidimensional general domain. The well-posedness is established under a monotone condition, and the exponential ergodicity is derived in the Wasserstein distance.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141289444","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
Isotropic random tangential vector fields on spheres 球面上的各向同性随机切向矢量场
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-03 DOI: 10.1016/j.spl.2024.110172
Tianshi Lu
{"title":"Isotropic random tangential vector fields on spheres","authors":"Tianshi Lu","doi":"10.1016/j.spl.2024.110172","DOIUrl":"10.1016/j.spl.2024.110172","url":null,"abstract":"<div><p>In this paper we characterized isotropic random tangential vector fields on <span><math><mi>d</mi></math></span>-spheres for <span><math><mrow><mi>d</mi><mo>≥</mo><mn>1</mn></mrow></math></span> by the cross-covariance, and derived their Karhunen–Loève expansion. The tangential vector field can be decomposed into a curl-free part and a divergence-free part by the Helmholtz–Hodge decomposition. We proved that the two parts can be correlated on a 2-sphere, while they must be uncorrelated on a <span><math><mi>d</mi></math></span>-sphere for <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. On a 3-sphere, the divergence-free part can be further decomposed into two isotropic flows.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141280781","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
Rate of convergence of trinomial formula to Black–Scholes formula 三项式公式与布莱克-斯科尔斯公式的收敛速度
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-06-01 DOI: 10.1016/j.spl.2024.110167
Yuttana Ratibenyakool , Kritsana Neammanee
{"title":"Rate of convergence of trinomial formula to Black–Scholes formula","authors":"Yuttana Ratibenyakool ,&nbsp;Kritsana Neammanee","doi":"10.1016/j.spl.2024.110167","DOIUrl":"10.1016/j.spl.2024.110167","url":null,"abstract":"<div><p>The Black–Scholes formula which was introduced by three economists, Black et al. (1973) has been widely used to calculate the theoretical price of the European call option. In 1979, Cox, Ross and Rubinstein (<span>Cox et al., 1979</span>) gave the binomial formula which is a tool to find the price of European option and showed that this formula converges to the Black–Scholes formula as the number of periods <span><math><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></math></span> converges to infinity. In 1988, Boyle investigated another formula that is used to find the price of European option, that is the trinomial formula. In 2015, Puspita et al. gave examples to show that the trinomial formula is closed to the Black–Scholes formula. After that, Ratibenyakool and Neammanee (2020) gave the rigorous proof of this convergence. In this paper, we show that the rate of convergence is of order <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></math></span>.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141281124","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
Some new asymptotic results for series estimation under clustered dependence 聚类依赖条件下序列估计的一些新渐近结果
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-28 DOI: 10.1016/j.spl.2024.110156
Pingbo Hu , Xiuyuan Peng , Xinglin Hu
{"title":"Some new asymptotic results for series estimation under clustered dependence","authors":"Pingbo Hu ,&nbsp;Xiuyuan Peng ,&nbsp;Xinglin Hu","doi":"10.1016/j.spl.2024.110156","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110156","url":null,"abstract":"<div><p>This paper presents some asymptotic results for series estimation of a nonparametric regression model under clustered dependence. A mean square rate of convergence for the series regression estimator is established. Moreover, asymptotic pointwise normality is shown for the series estimator.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141289443","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
Nonparametric inference for NBUE distributions based on the TTT transform 基于 TTT 变换的 NBUE 分布非参数推断
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-24 DOI: 10.1016/j.spl.2024.110157
Tommaso Lando
{"title":"Nonparametric inference for NBUE distributions based on the TTT transform","authors":"Tommaso Lando","doi":"10.1016/j.spl.2024.110157","DOIUrl":"10.1016/j.spl.2024.110157","url":null,"abstract":"<div><p>This paper presents a uniformly consistent estimator for the cumulative distribution function, operating under the assumption of “new better than used in expectation” (NBUE). Additionally, it introduces a novel class of consistent tests for the NBUE null hypothesis. Both procedures leverage the empirical total time on test (TTT) transform. Finite sample properties of the proposed methods are investigated through simulations.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141145311","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
Indeterminate Hamburger moment problem: Entropy convergence 不确定汉堡矩问题：熵收敛
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-17 DOI: 10.1016/j.spl.2024.110155
Pier Luigi Novi Inverardi , Aldo Tagliani , Mariyan Milev
{"title":"Indeterminate Hamburger moment problem: Entropy convergence","authors":"Pier Luigi Novi Inverardi ,&nbsp;Aldo Tagliani ,&nbsp;Mariyan Milev","doi":"10.1016/j.spl.2024.110155","DOIUrl":"10.1016/j.spl.2024.110155","url":null,"abstract":"<div><p>The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span>. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>h</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span> where the value of its entropy can be finite or <span><math><mrow><mo>−</mo><mi>∞</mi></mrow></math></span>.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141042948","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 distribution of argmaximum or a winner problem 最大值的分布或赢家问题
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-11 DOI: 10.1016/j.spl.2024.110152
Youri Davydov , Vladimir Rotar
{"title":"The distribution of argmaximum or a winner problem","authors":"Youri Davydov ,&nbsp;Vladimir Rotar","doi":"10.1016/j.spl.2024.110152","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110152","url":null,"abstract":"<div><p>We consider a limit theorem for the distribution of a random variable (r.v.) <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>arg</mo><msub><mrow><mo>max</mo></mrow><mrow><mi>i</mi><mo>:</mo><mn>1</mn><mo>…</mo><mi>n</mi></mrow></msub><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>’s are independent continuous non-negative random r.v.’s. The <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>i</mi><mo>=</mo><mn>1</mn><mo>.</mo><mo>…</mo><mo>,</mo><mi>n</mi></mrow></math></span>, may be interpreted as the gains of <span><math><mi>n</mi></math></span> players in a game, and the r.v. <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> itself as the number of a “winner”. The paper contains some limit theorems for the distribution of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> as <span><math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951460","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
Nonparametric kernel estimation of conditional copula density 条件共轭密度的非参数核估计
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-11 DOI: 10.1016/j.spl.2024.110154
Toihir Soulaimana Djaloud, Cheikh Tidiane Seck
{"title":"Nonparametric kernel estimation of conditional copula density","authors":"Toihir Soulaimana Djaloud,&nbsp;Cheikh Tidiane Seck","doi":"10.1016/j.spl.2024.110154","DOIUrl":"10.1016/j.spl.2024.110154","url":null,"abstract":"<div><p>This paper introduces a new mathematical formula for the bivariate conditional copula density and proposes kernel-type estimators for it. We demonstrate the consistency and asymptotic normality of these estimators, which also exhibit the best quadratic mean convergence rate when the optimal theoretical bandwidth is selected.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141032804","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-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises 在噪声中具有均场相互作用的扩散粒子最大值的大群体渐近论
IF 0.8 4区 数学
Statistics & Probability Letters Pub Date : 2024-05-10 DOI: 10.1016/j.spl.2024.110150
Nikolaos Kolliopoulos , David Sanchez , Amy Xiao
{"title":"Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises","authors":"Nikolaos Kolliopoulos ,&nbsp;David Sanchez ,&nbsp;Amy Xiao","doi":"10.1016/j.spl.2024.110150","DOIUrl":"https://doi.org/10.1016/j.spl.2024.110150","url":null,"abstract":"<div><p>We study the <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> limit of the normalized largest component in some systems of <span><math><mi>N</mi></math></span> diffusive particles with mean-field interaction. By applying a universal time change, the interaction in noises is transferred to the drift terms, and the asymptotic behavior of the maximum becomes well-understood due to existing results in the literature. We expect that the normalized maximum in the original setting has the same limiting distribution as that of i.i.d copies of a solution to the corresponding McKean–Vlasov SDE and we present some results and numerical simulations that support this conjecture.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001196/pdfft?md5=3ba9e929870a8e3c7e440260b4122bc0&pid=1-s2.0-S0167715224001196-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141067758","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
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