Annales De L Institut Henri Poincare-probabilites Et Statistiques最新文献_第6页

Precise intermittency for the parabolic Anderson equation with an $(1+1)$-dimensional time–space white noise 具有$(1+1)$维时空白噪声的抛物型安德森方程的精确间歇性

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-11-01 DOI: 10.1214/15-AIHP673

Xia Chen

{"title":"Precise intermittency for the parabolic Anderson equation with an $(1+1)$-dimensional time–space white noise","authors":"Xia Chen","doi":"10.1214/15-AIHP673","DOIUrl":"https://doi.org/10.1214/15-AIHP673","url":null,"abstract":"The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an (1 + 1)dimensional time–space white noise. Our main result positively confirms an open problem posted in (Ann. Probab. (2015) to appear) and originated from the observations made in the physical literature (J. Statist. Phys. 78 (1995) 1377–1401) and (Nuclear Physics B 290 (1987) 582–602). By a link through the Feynman–Kac’s formula, our theorem leads to the evaluation of the ground state energy for the n-body problem with Dirac pair interaction. Résumé. Nous calculons les moments de l’exposant de Lyapunov de la solution de l’équation d’Anderson parabolique avec un bruit blanc en espace–temps en dimension (1 + 1). Notre résultat principal confirme un problème ouvert posé dans (Ann. Probab. (2015) à paraître) et basé sur des observations faites dans la littérature physique (J. Statist. Phys. 78 (1995) 1377–1401) et (Nuclear Physics B 290 (1987) 582–602). À travers la formule de Feynman–Kac, notre théorème permet l’évaluation de l’état fondamental pour le problème à n-corps avec interaction de Dirac par paires. MSC: 60F10; 60H15; 60H40; 60J65; 81U10","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"24 1","pages":"1486-1499"},"PeriodicalIF":1.5,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78981691","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: 50

Exponential asymptotics for time–space Hamiltonians 时空哈密顿量的指数渐近性

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-11-01 DOI: 10.1214/13-AIHP588

Xia Chen, Yaozhong Hu, Jiancheng Song, Fei Xing

引用次数: 38

The power of averaging at two consecutive time steps: Proof of a mixing conjecture by Aldous and Fill 两个连续时间步的平均能力:Aldous和Fill的混合猜想的证明

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-08-19 DOI: 10.1214/16-AIHP782

J. Hermon, Y. Peres

{"title":"The power of averaging at two consecutive time steps: Proof of a mixing conjecture by Aldous and Fill","authors":"J. Hermon, Y. Peres","doi":"10.1214/16-AIHP782","DOIUrl":"https://doi.org/10.1214/16-AIHP782","url":null,"abstract":"Let $(X_t)_{t = 0 }^{infty}$ be an irreducible reversible discrete time Markov chain on a finite state space $Omega $. Denote its transition matrix by $P$. To avoid periodicity issues (and thus ensuring convergence to equilibrium) one often considers the continuous-time version of the chain $(X_t^{mathrm{c}})_{t ge 0} $ whose kernel is given by $H_t:=e^{-t}sum_k (tP)^k/k! $. Another possibility is to consider the associated averaged chain $(X_t^{mathrm{ave}})_{t = 0}^{infty}$, whose distribution at time $t$ is obtained by replacing $P$ by $A_t:=(P^t+P^{t+1})/2$. \u0000A sequence of Markov chains is said to exhibit (total-variation) cutoff if the convergence to stationarity in total-variation distance is abrupt. Let $(X_t^{(n)})_{t = 0 }^{infty}$ be a sequence of irreducible reversible discrete time Markov chains. In this work we prove that the sequence of associated continuous-time chains exhibits total-variation cutoff around time $t_n$ iff the sequence of the associated averaged chains exhibits total-variation cutoff around time $t_n$. Moreover, we show that the width of the cutoff window for the sequence of associated averaged chains is at most that of the sequence of associated continuous-time chains. In fact, we establish more precise quantitative relations between the mixing-times of the continuous-time and the averaged versions of a reversible Markov chain, which provide an affirmative answer to a problem raised by Aldous and Fill.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"78 1 1","pages":"2030-2042"},"PeriodicalIF":1.5,"publicationDate":"2015-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78290058","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: 8

A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations 一般过滤中BSDEs超解先验估计的统一方法

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-07-23 DOI: 10.1214/16-AIHP798

B. Bouchard, Dylan Possamai, Xiaolu Tan, Chao Zhou

引用次数: 42

Non-fixation for biased Activated Random Walks 偏置激活随机漫步的非固定

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-07-16 DOI: 10.1214/17-AIHP827

L. Rolla, L. Tournier

引用次数: 15

The spans in Brownian motion 布朗运动的跨度

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-06-05 DOI: 10.1214/16-AIHP749

S. Evans, J. Pitman, Wenpin Tang

引用次数: 1

BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data 具有扩散约束的BSDEs和具有无界数据的粘性Hamilton-Jacobi方程

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-05-26 DOI: 10.1214/16-AIHP762

Andrea Cosso, H. Pham, Hao Xing

引用次数: 8

Nonexistence of Lyapunov exponents for matrix cocycles 矩阵共环的Lyapunov指数的不存在性

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-05-18 DOI: 10.1214/15-AIHP733

Xueting Tian

引用次数: 11

Monotonicity and condensation in homogeneous stochastic particle systems 均匀随机粒子系统的单调性和凝聚性

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-05-08 DOI: 10.1214/17-AIHP821

T. Rafferty, P. Chleboun, S. Grosskinsky

引用次数: 10

Parametric first-order Edgeworth expansion for Markov additive functionals. Application to $M$-estimations 马尔可夫加性泛函的参数一阶Edgeworth展开。应用于$M$-估计

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-05-01 DOI: 10.1214/13-AIHP592

D. Ferre

{"title":"Parametric first-order Edgeworth expansion for Markov additive functionals. Application to $M$-estimations","authors":"D. Ferre","doi":"10.1214/13-AIHP592","DOIUrl":"https://doi.org/10.1214/13-AIHP592","url":null,"abstract":"We give a spectral approach to prove a parametric first-order Edgeworth expansion for bivariate additive functionals of strongly ergodic Markov chains. In particular, given any V -geometrically ergodic Markov chain (Xn)n∈N whose distribution depends on a parameter θ , we prove that {ξp(Xn−1,Xn);p ∈P, n ≥ 1} satisfies a uniform (in (θ,p)) first-order Edgeworth expansion provided that {ξp(·, ·);p ∈ P} satisfies some non-lattice condition and an almost optimal moment domination condition. Furthermore, the sequence (Xn)n∈N need not be stationary. This result is applied to M-estimators of Markov chains and in particular of V -geometrically ergodic Markov chains. The M-estimators of some autoregressive processes are studied. Résumé. Grâce à une approche spectrale, nous donnons des conditions assurant la validité du développement d’Edgeworth d’ordre 1 paramétrique, dans le cadre général des fonctionnelles bivariées et additives de chaînes de Markov fortement ergodiques. En particulier, soit (Xn)n∈N une chaîne de Markov V -géométriquement ergodique dont la loi dépend d’un paramètre θ . Nous montrons alors que {ξp(Xn−1,Xn);p ∈P, n ≥ 1} satisfait un développement d’Edgeworth d’ordre 1 uniforme (en (θ,p)) si {ξp(·, ·);p ∈P} satisfait une condition de type non-lattice ainsi qu’une condition quasi-optimale de moment-domination. De plus, ce résultat est établi dans le cas où les données (Xn)n∈N ne sont pas nécessairement stationnaires. Ce résultat est appliqué en particulier aux M-estimateurs associés à des chaînes de Markov V -géométriquement ergodiques. Les M-estimateurs de processus autorégressifs sont étudiés. MSC: 60F05; 60J05; 62F12; 62M05","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"82 1","pages":"781-808"},"PeriodicalIF":1.5,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86844498","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