Annals of Applied Probability最新文献_第4页

Nearly optimal central limit theorem and bootstrap approximations in high dimensions 高维的近最优中心极限定理和自举近似

2区数学

Annals of Applied Probability Pub Date : 2023-06-01 DOI: 10.1214/22-aap1870

Victor Chernozhukov, Denis Chetverikov, Yuta Koike

引用次数: 1

Quenched and averaged large deviations for random walks in random environments: The impact of disorder 随机环境中随机行走的淬火和平均大偏差：无序的影响

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-06-01 DOI: 10.1214/22-aap1864

Rodrigo A. Bazaes, Chiranjib Mukherjee, A. Ramírez, S. Saglietti

{"title":"Quenched and averaged large deviations for random walks in random environments: The impact of disorder","authors":"Rodrigo A. Bazaes, Chiranjib Mukherjee, A. Ramírez, S. Saglietti","doi":"10.1214/22-aap1864","DOIUrl":"https://doi.org/10.1214/22-aap1864","url":null,"abstract":"In 2003, Varadhan ( Comm. Pure Appl. Math. 56 (2003) 1222–1245) developed a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on Z d . One fundamental question which remained open was to determine when the quenched and averaged large deviation rate functions agree, and when they do not. In this article we show that for RWRE in uniformly elliptic and i.i.d. environment in d ≥ 4, the two rate functions agree on any compact set contained in the interior of their domain which does not contain the origin, provided that the disorder of the environment is sufﬁciently low. Our result provides a new formulation which encompasses a set of sufﬁcient conditions under which these rate functions agree without assuming that the RWRE is ballistic (see ( Probab. Theory Related Fields 149 (2011) 463–491)), satisﬁes a CLT or even a law of large numbers ( Electron. Commun. Probab. 7 (2002)191–197; Ann. Probab. 36 (2008) 728–738). Also, the equality of rate functions is not restricted to neighborhoods around given points, as long as the disorder of the environment is kept low. One of the novelties of our approach is the introduction of an auxiliary random walk in a deterministic environment which is itself ballistic (regardless of the actual RWRE behavior) and whose large deviation properties approximate those of the original RWRE in a robust manner, even if the original RWRE is not ballistic itself.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42911546","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: 1

The spatial Λ-Fleming–Viot process in a random environment 随机环境中的空间∧-Feming–Viot过程

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-06-01 DOI: 10.1214/22-aap1871

A. Klimek, T. Rosati

引用次数: 0

Nonparametric learning for impulse control problems—Exploration vs. exploitation 冲动控制问题的非参数学习:探索与利用

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-04-01 DOI: 10.1214/22-aap1849

S. Christensen, C. Strauch

{"title":"Nonparametric learning for impulse control problems—Exploration vs. exploitation","authors":"S. Christensen, C. Strauch","doi":"10.1214/22-aap1849","DOIUrl":"https://doi.org/10.1214/22-aap1849","url":null,"abstract":"One of the fundamental assumptions in stochastic control of continuous time processes is that the dynamics of the underlying (diﬀu-sion) process is known. This is, however, usually obviously not fulﬁlled in practice. On the other hand, over the last decades, a rich theory for nonparametric estimation of the drift (and volatility) for continuous time processes has been developed. The aim of this paper is bringing together techniques from stochastic control with methods from statistics for stochastic processes to ﬁnd a way to both learn the dynamics of the underlying process and control in a reasonable way at the same time. More precisely, we study a long-term average impulse control problem, a stochastic version of the classical Faustmann timber harvesting problem. One of the problems that immediately arises is an exploration-exploitation dilemma as is well known for problems in machine learning. We propose a way to deal with this issue by combining exploration and exploitation periods in a suitable way. Our main ﬁnding is that this construction can be based on the rates of convergence of estimators for the invariant density. Using this, we obtain that the average cumulated regret is of uniform order O ( T − 1 / 3 ).","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44358595","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

The maximum of branching Brownian motion in Rd Rd中分支布朗运动的极大值

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-04-01 DOI: 10.1214/22-aap1848

Yujin H. Kim, E. Lubetzky, O. Zeitouni

引用次数: 4

A Kesten–Stigum type theorem for a supercritical multitype branching process in a random environment 随机环境下超临界多型分支过程的Kesten-Stigum型定理

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-04-01 DOI: 10.1214/22-aap1840

I. Grama, Quansheng Liu, Erwan Pin

{"title":"A Kesten–Stigum type theorem for a supercritical multitype branching process in a random environment","authors":"I. Grama, Quansheng Liu, Erwan Pin","doi":"10.1214/22-aap1840","DOIUrl":"https://doi.org/10.1214/22-aap1840","url":null,"abstract":"Abstract. Consider a multi-type branching process in a random environment, whose reproduction law of generation n depends on the random environment at time n, unlike a constant distribution assumed in the Galton-Watson process. The famous Kesten-Stigum theorem for a supercritical multi-type Galton-Watson process gives a precise description of the exponential increasing rate of the population size via a criterion for the non-degeneracy of the fundamental martingale. Finding the corresponding result in the random environment case is a longstanding problem. For the single-type case the problem has been solved by Athreya and Karlin (1971) and Tanny (1988), but for the multi-type case it has been open for 50 years. Here we solve this problem in the typical case, by constructing a suitable martingale which reduces to the fundamental one in the constat environment case, and by establishing a criterion for the non-degeneracy of its limit. The convergence in law of the direction of the branching process is also considered. Our results open ways in establishing other limit theorems, such as law of large numbers, central limit theorems, Berry-Essen bound, and large deviation results.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43167226","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

Large-scale behaviour and hydrodynamic limit of beta coalescents β聚结剂的大尺度行为和流体动力学极限

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-02-01 DOI: 10.1214/22-aap1782

Luke Miller, Helmut H. Pitters

引用次数: 0

On a nonlinear SPDE derived from a hydrodynamic limit in a Sinai-type random environment 关于sinai型随机环境中由水动力极限导出的非线性SPDE

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2023-02-01 DOI: 10.1214/22-aap1813

C. Landim, Carlos G. Pacheco, S. Sethuraman, Jianfei Xue

引用次数: 0

Weak and strong error analysis for mean-field rank-based particle approximations of one-dimensional viscous scalar conservation laws 一维粘性标量守恒律平均场秩基粒子近似的弱、强误差分析

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2022-12-01 DOI: 10.1214/21-aap1776

Oumaima Bencheikh, B. Jourdain

引用次数: 3

Properties of eigenvalues and eigenvectors of large-dimensional sample correlation matrices 高维样本相关矩阵的特征值和特征向量的性质

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2022-12-01 DOI: 10.1214/22-aap1802

Yanqing Yin, Yanyuan Ma

{"title":"Properties of eigenvalues and eigenvectors of large-dimensional sample correlation matrices","authors":"Yanqing Yin, Yanyuan Ma","doi":"10.1214/22-aap1802","DOIUrl":"https://doi.org/10.1214/22-aap1802","url":null,"abstract":"This paper is to study the properties of eigenvalues and eigenvectors of high dimensional sample correlation matrices. We firstly improve the result of Jiang (2004); Xiao and Zhou (2010) and the Theorem 1 of Karoui (2009), both concerning the limiting spectral distribution and the extreme eigenvalues of sample correlation matrices, by allowing a more general fourth moment condition. Then, we establish a central limit theorem (CLT) for the linear statistics of the eigenvectors of large sample correlation matrices. We discover that the difference between the functional CLT of the sample covariance matrix and that of the sample correlation matrix is fundamentally influenced by the direction of a nonrandom projection vector. In the special case where the square root of the correlation matrix is identity, the difference will be determined by the sum of the fourth powers of the entries of the projection vector. These results also indicate that the eigenmatrix of sample correlation matrix is not asymptotic Haar if the underlying distribution is Gaussian. In other words, the normalization based on the sample variances affects the asymptotic properties of the eigenmatrix of the Wishart matrix. Furthermore, we establish a theorem concerning CLT for the linear statistics of the eigenvectors of large sample covariance matrices. This theorem improves the main result in Bai, Miao, and Pan (2007), which requires the assumption that the fourth moment of the underlying variable matches the one of Gaussian distribution, as well as Theorem 1.3 in Pan and Zhou (2008), which relaxes the Gaussian like fourth moment requirement but assumes the maximum entries of the projection vectors converge to 0 (i.e. the `∞ norms of the projection vectors converge to 0). We illustrate the usefulness of the theoretical results through an application in communications.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49091572","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