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Annales De L Institut Henri Poincare-probabilites Et Statistiques最新文献

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Parabolic Anderson model with a fractional Gaussian noise that is rough in time 具有分数高斯噪声的抛物型安德森模型在时间上是粗糙的
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-05-01 DOI: 10.1214/19-aihp983
Xia Chen
{"title":"Parabolic Anderson model with a fractional Gaussian noise that is rough in time","authors":"Xia Chen","doi":"10.1214/19-aihp983","DOIUrl":"https://doi.org/10.1214/19-aihp983","url":null,"abstract":"This paper concerns the parabolic Anderson equation ∂u ∂t = 1 2 ∆u+ u ∂d+1WH ∂t∂x1 · · · ∂xd generated by a (d + 1)-dimensional fractional noise with the Hurst parameter H = (H0, H1, · · · , Hd) with special interest in the setting that some of H0, · · · , Hd are less than half. In the recent work [9], the case of the spatial roughness has been investigated. To put the last piece of the puzzle in place, this work investigates the case when H0 < 1/2 with the concern on solvability, Feynman-Kac’s moment formula and intermittency of the system. Key-words: parabolic Anderson equation, Dalang’s condition, fractional, rough and critical Gaussian noises, Feynman-Kac’s representation, Brownian motion, moment asymptotics AMS subject classification (2010): 60F10, 60H15, 60H40, 60J65, 81U10. ∗Research partially supported by the Simons Foundation #585506. 1","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"36 1","pages":"792-825"},"PeriodicalIF":1.5,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82202479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 13
A Central Limit Theorem for Wasserstein type distances between two distinct univariate distributions 两个不同单变量分布间Wasserstein型距离的中心极限定理
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-05-01 DOI: 10.1214/19-aihp990
Philippe Berthet, J. Fort, T. Klein
{"title":"A Central Limit Theorem for Wasserstein type distances between two distinct univariate distributions","authors":"Philippe Berthet, J. Fort, T. Klein","doi":"10.1214/19-aihp990","DOIUrl":"https://doi.org/10.1214/19-aihp990","url":null,"abstract":"In this article we study the natural nonparametric estimator of a Wasserstein type cost between two distinct continuous distributions Fand G on R. The estimator is based on the order statistics of a sample having marginals F, G and any joint distribution. We prove a central limit theorem under general conditions relating the tails and the cost function. In particular, these conditions are satisfied by Wasserstein distances of order p>1and compatible classical probability distributions.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"34 1","pages":"954-982"},"PeriodicalIF":1.5,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86479892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 2
Errata for Perturbation by non-local operators 非局部算子摄动的勘误表
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-02-01 DOI: 10.1214/20-aihp1045
Zhen-Qing Chen, Jie-Ming Wang
{"title":"Errata for Perturbation by non-local operators","authors":"Zhen-Qing Chen, Jie-Ming Wang","doi":"10.1214/20-aihp1045","DOIUrl":"https://doi.org/10.1214/20-aihp1045","url":null,"abstract":"","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"81 1","pages":"760-763"},"PeriodicalIF":1.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74880770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
New lower bounds for trace reconstruction 新的轨迹重建下界
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2019-05-08 DOI: 10.1214/20-AIHP1089
Zachary Chase
{"title":"New lower bounds for trace reconstruction","authors":"Zachary Chase","doi":"10.1214/20-AIHP1089","DOIUrl":"https://doi.org/10.1214/20-AIHP1089","url":null,"abstract":"We improve the lower bound on worst case trace reconstruction from Ω(n5/4logn) to Ω(n3/2log7n). As a consequence, we improve the lower bound on average case trace reconstruction from Ω(log9/4n loglogn) to Ω(log5/2n(loglogn)7).","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"20 1","pages":"627-643"},"PeriodicalIF":1.5,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82008074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 37
Support theorem for a singular SPDE: The case of gPAM 奇异SPDE的支持定理:gPAM的情况
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2018-02-01 DOI: 10.1214/16-AIHP800
K. Chouk, P. Friz
{"title":"Support theorem for a singular SPDE: The case of gPAM","authors":"K. Chouk, P. Friz","doi":"10.1214/16-AIHP800","DOIUrl":"https://doi.org/10.1214/16-AIHP800","url":null,"abstract":"","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"32 1","pages":"202-219"},"PeriodicalIF":1.5,"publicationDate":"2018-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83536850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 12
Pólya tree posterior distributions on densities Pólya密度的树后验分布
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-11-01 DOI: 10.1214/16-AIHP784
I. Castillo
{"title":"Pólya tree posterior distributions on densities","authors":"I. Castillo","doi":"10.1214/16-AIHP784","DOIUrl":"https://doi.org/10.1214/16-AIHP784","url":null,"abstract":". Pólya trees form a popular class of prior distributions used in Bayesian nonparametrics. For some choice of parameters, Pólya trees are prior distributions on density functions. In this paper we carry out a frequentist analysis of the induced posterior distributions in the density estimation model. We investigate the contraction rate of Pólya tree posterior densities in terms of the supremum loss and study the limiting shape distribution. A nonparametric Bernstein–von Mises theorem is established, as well as a Bayesian Donsker theorem for the posterior cumulative distribution function. Résumé. Les arbres de Pólya constituent une classe de lois a priori très utilisée en bayésien non-paramétrique. Pour certains choix de paramètres, les arbres de Pólya induisent des lois à densité. Nous menons une analyse fréquentiste des lois a posteriori bayésiennes correspondantes dans le modèle d’estimation de densité. La concentration a posteriori des densités–arbre de Pólya est étudiée en terme de la norme–sup et nous déterminons la loi a posteriori limite après renormalisation. Un théorème de Bernstein– von Mises non-paramétrique est établi, ainsi qu’un théorème de Donsker bayésien pour la fonction de répartition a posteriori.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"119 1","pages":"2074-2102"},"PeriodicalIF":1.5,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73639574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 28
Limit theorems for the left random walk on $operatorname{GL}_{d}(mathbb{R})$
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-11-01 DOI: 10.1214/16-AIHP773
C. Cuny, J. Dedecker, Christophe Jan
{"title":"Limit theorems for the left random walk on $operatorname{GL}_{d}(mathbb{R})$","authors":"C. Cuny, J. Dedecker, Christophe Jan","doi":"10.1214/16-AIHP773","DOIUrl":"https://doi.org/10.1214/16-AIHP773","url":null,"abstract":"","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"45 1","pages":"1839-1865"},"PeriodicalIF":1.5,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76715329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Sampling of probability measures in the convex order by Wasserstein projection 用Wasserstein投影对概率测度进行凸序抽样
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-09-15 DOI: 10.1214/19-AIHP1014
A. Alfonsi, Jacopo Corbetta, B. Jourdain
{"title":"Sampling of probability measures in the convex order by Wasserstein projection","authors":"A. Alfonsi, Jacopo Corbetta, B. Jourdain","doi":"10.1214/19-AIHP1014","DOIUrl":"https://doi.org/10.1214/19-AIHP1014","url":null,"abstract":"In this paper, for $mu$ and $nu$ two probability measures on $mathbb{R}^d$ with finite moments of order $rhoge 1$, we define the respective projections for the $W_rho$-Wasserstein distance of $mu$ and $nu$ on the sets of probability measures dominated by $nu$ and of probability measures larger than $mu$ in the convex order. The $W_2$-projection of $mu$ can be easily computed when $mu$ and $nu$ have finite support by solving a quadratic optimization problem with linear constraints. In dimension $d=1$, Gozlan et al.~(2018) have shown that the projections do not depend on $rho$. We explicit their quantile functions in terms of those of $mu$ and $nu$. The motivation is the design of sampling techniques preserving the convex order in order to approximate Martingale Optimal Transport problems by using linear programming solvers. We prove convergence of the Wasserstein projection based sampling methods as the sample sizes tend to infinity and illustrate them by numerical experiments.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"62 1","pages":"1706-1729"},"PeriodicalIF":1.5,"publicationDate":"2017-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82782972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 30
Ergodicity for multidimensional jump diffusions with position dependent jump rate 具有位置依赖跳跃速率的多维跳跃扩散的遍历性
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-08-01 DOI: 10.1214/16-AIHP750
E. Löcherbach, V. Rabiet
{"title":"Ergodicity for multidimensional jump diffusions with position dependent jump rate","authors":"E. Löcherbach, V. Rabiet","doi":"10.1214/16-AIHP750","DOIUrl":"https://doi.org/10.1214/16-AIHP750","url":null,"abstract":"We consider a jump type diffusion X = (Xt) with infinitesimal generator given by Lψ(x) = 1/2 ∑ a ij (x) ∂2 ψ(x)/∂x i ∂x j + g(x)∇ψ(x) + ∫ (ψ(x + c(z, x)) − ψ(x))γ(z, x)µ(dz) where µ is of infinite total mass. We prove Harris recurrence of X using a regeneration scheme which is entirely based on the jumps of the process. Moreover we state explicit conditions in terms of the coefficients of the process allowing to control the speed of convergence to equilibrium in terms of deviation inequalities for integrable additive functionals.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"58 1","pages":"1136-1163"},"PeriodicalIF":1.5,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73436271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 6
Moment asymptotics for parabolic Anderson equation with fractional time-space noise: In Skorokhod regime 具有分数时空噪声的抛物型Anderson方程的矩渐近性:在Skorokhod域中
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-05-01 DOI: 10.1214/15-AIHP738
Xia Chen
{"title":"Moment asymptotics for parabolic Anderson equation with fractional time-space noise: In Skorokhod regime","authors":"Xia Chen","doi":"10.1214/15-AIHP738","DOIUrl":"https://doi.org/10.1214/15-AIHP738","url":null,"abstract":". In this paper, we consider the parabolic Anderson equation that is driven by a Gaussian noise fractional in time and white or fractional in space, and is solved in a mild sense defined by Skorokhod integral. Our objective is the precise moment Lyapunov exponent and high moment asymptotics. As far as the long term asymptotics are concerned, some feature given in our theorems is different from what have been observed in the Stratonovich-regime and in the setting of the white time noise. While the difference disappears when it comes to the high moment asymptotics. To achieve our goal, we introduce a variational inequality and use some newly developed tools such as time-space LDP of Feynman–Kac type, linearization by tangent approximation, together with some techniques developed along the line of probability in Banach spaces. Résumé. lorsque l’on considère les asymptotiques des grands moments. Nos résultats sont obtenus en introduisant une nouvelle inégalité variationnelle, et à l’aide d’outils nouveaux tels qu’un principe de grandes déviations de type Feynman–Kac, la linéarisation par des approximations tangentes, et des techniques inspirées des probabilités dans les espaces de Banach. MSC:","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"8 1","pages":"819-841"},"PeriodicalIF":1.5,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88806318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 30
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