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

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Conditional distributions, exchangeable particle systems, and stochastic partial differential equations 条件分布，可交换粒子系统，和随机偏微分方程
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-08-01 DOI: 10.1214/13-AIHP543
D. Crisan, T. Kurtz, Yoonjung Lee
{"title":"Conditional distributions, exchangeable particle systems, and stochastic partial differential equations","authors":"D. Crisan, T. Kurtz, Yoonjung Lee","doi":"10.1214/13-AIHP543","DOIUrl":"https://doi.org/10.1214/13-AIHP543","url":null,"abstract":"Stochastic partial dierential equations whose solutions are probability-measurevalued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of innite exchangeable systems of particles and as the solutions for ltering problems. In both these cases, the solution is the conditional distribution of the solution of a stochastic dierential equation. The main result states that, under mild nondegeneracy conditions on the coecients of the stochastic dierential equation, the conditional distribution of its solution charges any open set. Under stronger conditions we show that it is absolutely continuous with respect to Lebesgue measure and its density is positive almost everywhere. As applications we show the existence of a solution of a system of interacting diusions and study the properties of the solution of the nonlinear ltering equation within a framework that allows for the signal noise and the observation noise to be correlated. The work was motivated by a model of asset price determination in which the price is given as a quantile of the valuations of innitely many individual investors. MSC 2010 subject classications: 60H15, 60G09, 60G35, 60J25","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"103 1","pages":"946-974"},"PeriodicalIF":1.5,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91005837","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: 20
Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation 非马尔可夫扩散的大偏差和路径相关的Eikonal方程
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-07-20 DOI: 10.1214/15-AIHP678
Jingsheng Ma, Zhenjie Ren, N. Touzi, Jianfeng Zhang
{"title":"Large deviations for non-Markovian diffusions and a path-dependent Eikonal equation","authors":"Jingsheng Ma, Zhenjie Ren, N. Touzi, Jianfeng Zhang","doi":"10.1214/15-AIHP678","DOIUrl":"https://doi.org/10.1214/15-AIHP678","url":null,"abstract":"This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a different line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using backward stochastic differential techniques. Similar to the Markovian case, we obtain a characterization of the action function as the unique bounded solution of a path-dependent version of the Eikonal equation. Finally, we provide an application to the short maturity asymptotics of the implied volatility surface in financial mathematics.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"15 1","pages":"1196-1216"},"PeriodicalIF":1.5,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88907199","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: 11
Total length of the genealogical tree for quadratic stationary continuous-state branching processes 二次平稳连续状态分支过程谱系树的总长度
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-07-17 DOI: 10.1214/15-AIHP683
Hongwei Bi, Jean-François Delmas
{"title":"Total length of the genealogical tree for quadratic stationary continuous-state branching processes","authors":"Hongwei Bi, Jean-François Delmas","doi":"10.1214/15-AIHP683","DOIUrl":"https://doi.org/10.1214/15-AIHP683","url":null,"abstract":"We prove the existence of the total length process for the genealogical tree of a population model with random size given by a quadratic stationary continuous-state branching processes. We also give, for the one-dimensional marginal, its Laplace transform as well as the fluctuation of the corresponding convergence. This result is to be compared with the one obtained by Pfaffelhuber and Wakolbinger for constant size population associated to the Kingman coalescent. We also give a time reversal property of the number of ancestors process at all time, and give a description of the so-called lineage tree in this model.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"65 1","pages":"1321-1350"},"PeriodicalIF":1.5,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85301736","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: 9
Any orthonormal basis in high dimension is uniformly distributed over the sphere 任何高维正交基都均匀分布在球面上
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-06-10 DOI: 10.1214/15-AIHP732
S. Goldstein, J. Lebowitz, R. Tumulka, N. Zanghí
{"title":"Any orthonormal basis in high dimension is uniformly distributed over the sphere","authors":"S. Goldstein, J. Lebowitz, R. Tumulka, N. Zanghí","doi":"10.1214/15-AIHP732","DOIUrl":"https://doi.org/10.1214/15-AIHP732","url":null,"abstract":"Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately uniformly distributed over the sphere by choosing a partition A1,...,Am of S(X) and checking whether the fraction of points in B that lie in Ak is close to u(Ak) for each k = 1,...,m. We show that if B is any orthonormal basis of X and m is not too large, then, if we randomize the test by applying a random rotation to the sets A1,...,Am, B will pass the random test with probability close to 1. This statement is related to, but not entailed by, the law of large numbers. An application of this fact in quantum statistical mechanics is briefly described.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"155 1","pages":"701-717"},"PeriodicalIF":1.5,"publicationDate":"2014-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79625946","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
Liouville heat kernel: Regularity and bounds 刘维尔热核:规律性和界限
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-06-02 DOI: 10.1214/15-AIHP676
Pascal Maillard, Rémi Rhodes, V. Vargas, O. Zeitouni
{"title":"Liouville heat kernel: Regularity and bounds","authors":"Pascal Maillard, Rémi Rhodes, V. Vargas, O. Zeitouni","doi":"10.1214/15-AIHP676","DOIUrl":"https://doi.org/10.1214/15-AIHP676","url":null,"abstract":"Dans ce papier, nous initions l’etude des proprietes analytiques du noyau de la chaleur de Liouville. En particulier, nous etablissons des estimees de regularite pour le noyau et nous l’encadrons par des bornes inferieures et superieures non triviales.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"98 1","pages":"1281-1320"},"PeriodicalIF":1.5,"publicationDate":"2014-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77027313","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: 32
Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome? 阈值窗口的缩放限制:单调布尔函数何时翻转其结果?
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-05-28 DOI: 10.1214/16-AIHP786
Daniel Ahlberg, J. Steif, G. Pete
{"title":"Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?","authors":"Daniel Ahlberg, J. Steif, G. Pete","doi":"10.1214/16-AIHP786","DOIUrl":"https://doi.org/10.1214/16-AIHP786","url":null,"abstract":"Consider a monotone Boolean function f:{0,1}^n to {0,1} and the canonical monotone coupling \u0000{eta_p:p in [0,1]} of an element in {0,1}^n chosen according to product measure with intensity \u0000p in [0,1]. The random point p in [0,1] where f(eta_p) flips from 0 to 1 is often concentrated \u0000near a particular point, thus exhibiting a threshold phenomenon. For a sequence of such Boolean functions, \u0000we peer closely into this threshold window and consider, for large n, the limiting distribution (properly \u0000normalized to be nondegenerate) of this random point where the Boolean function switches from being 0 to 1. \u0000We determine this distribution for a number of the Boolean functions which are typically studied and pay \u0000particular attention to the functions corresponding to iterated majorityand percolation crossings. It turns out \u0000that these limiting distributions have quite varying behavior. In fact, we show that any nondegenerate \u0000probability measure on R arises in this way for some sequence of Boolean functions.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"75 1","pages":"2135-2161"},"PeriodicalIF":1.5,"publicationDate":"2014-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90678978","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
Long time behaviour and stationary regime of memory gradient diffusions 记忆梯度扩散的长时间行为和平稳状态
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-05-01 DOI: 10.1214/12-AIHP536
S. Gadat, Fabien Panloup
{"title":"Long time behaviour and stationary regime of memory gradient diffusions","authors":"S. Gadat, Fabien Panloup","doi":"10.1214/12-AIHP536","DOIUrl":"https://doi.org/10.1214/12-AIHP536","url":null,"abstract":"In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the marginal distribution, to the associated steady regimes. When the memory is too long, we show that in general, the dynamical system has a tendency to explode, and in the particular Gaussian case, we explicitly obtain the rate of divergence.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"2016 1","pages":"564-601"},"PeriodicalIF":1.5,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86526836","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: 21
Comparison between two types of large sample covariance matrices 两类大样本协方差矩阵的比较
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-05-01 DOI: 10.1214/12-AIHP506
G. Pan
{"title":"Comparison between two types of large sample covariance matrices","authors":"G. Pan","doi":"10.1214/12-AIHP506","DOIUrl":"https://doi.org/10.1214/12-AIHP506","url":null,"abstract":"Let {X ij }, i, j = · · · , be a double array of independent and identically distributed (i.i.d.) real random variables with EX 11 = µ, E|X 11 − µ| 2 = 1 and E|X 11 | 4 < ∞. Consider sample covariance matrices (with/without empirical centering) S = 1 n n j=1 (s j − ¯ s)(s j − ¯ s) T and S = 1 n n j=1 s j s T j , where ¯ s = 1 n n j=1 s j and s j = T 1/2 n (X 1j , · · · , X pj) T with (T 1/2 n) 2 = T n , non-random symmetric non-negative definite matrix. It is proved that central limit theorems of eigenvalue statistics of S and S are different as n → ∞ with p/n approaching a positive constant. Moreover , it is also proved that such a different behavior is not observed in the average behavior of eigenvectors.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"15 1","pages":"655-677"},"PeriodicalIF":1.5,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87010067","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: 35
A Uniform Dimension Result for Two-Dimensional Fractional Multiplicative Processes 二维分数阶乘法过程的一致维数结果
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-05-01 DOI: 10.1214/12-AIHP509
Xiong Jin
{"title":"A Uniform Dimension Result for Two-Dimensional Fractional Multiplicative Processes","authors":"Xiong Jin","doi":"10.1214/12-AIHP509","DOIUrl":"https://doi.org/10.1214/12-AIHP509","url":null,"abstract":"Given a two-dimensional fractional multiplicative process (Ft)t∈[0,1] determined by two Hurst exponents H1 and H2, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [0, 1] by F if and only if H1 = H2.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"97 1","pages":"512-523"},"PeriodicalIF":1.5,"publicationDate":"2014-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79027230","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
On the Malliavin differentiability of BSDEs 关于BSDEs的Malliavin可微性
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-04-03 DOI: 10.1214/15-AIHP723
Thibaut Mastrolia, Dylan Possamai, Anthony R'eveillac
{"title":"On the Malliavin differentiability of BSDEs","authors":"Thibaut Mastrolia, Dylan Possamai, Anthony R'eveillac","doi":"10.1214/15-AIHP723","DOIUrl":"https://doi.org/10.1214/15-AIHP723","url":null,"abstract":"In this paper we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. Our results rely on the interpretation of the Malliavin derivative as a Gâteaux derivative in the directions of the Cameron-Martin space. Incidentally , we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces $D^{1,p}$ .","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"83 1","pages":"464-492"},"PeriodicalIF":1.5,"publicationDate":"2014-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88907426","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: 18
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