Annals of Probability最新文献_第10页

Strong invariance and noise-comparison principles for some parabolic stochastic PDEs 一些抛物型随机偏微分方程的强不变性和噪声比较原理

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-04-28 DOI: 10.1214/15-AOP1009

Mathew Joseph, D. Khoshnevisan, C. Mueller

引用次数: 15

Recurrence and transience for the frog model on trees 树形青蛙模型的递归性和暂态性

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-04-24 DOI: 10.1214/16-AOP1125

C. Hoffman, Tobias Johnson, M. Junge

引用次数: 61

Invariance principle for variable speed random walks on trees 树上变速随机行走的不变性原理

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-04-24 DOI: 10.1214/15-AOP1071

S. Athreya, Wolfgang Lohr, A. Winter

{"title":"Invariance principle for variable speed random walks on trees","authors":"S. Athreya, Wolfgang Lohr, A. Winter","doi":"10.1214/15-AOP1071","DOIUrl":"https://doi.org/10.1214/15-AOP1071","url":null,"abstract":"We consider stochastic processes on complete, locally compact tree-like metric spaces (T,r)(T,r) on their “natural scale” with boundedly finite speed measure νν. Given a triple (T,r,ν)(T,r,ν) such a speed-νν motion on (T,r)(T,r) can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all x,y∈Tx,y∈T and all positive, bounded measurable ff, \u0000 \u0000Ex[∫τy0dsf(Xs)]=2∫Tν(dz)r(y,c(x,y,z))f(z)<∞, \u0000Ex[∫0τydsf(Xs)]=2∫Tν(dz)r(y,c(x,y,z))f(z)<∞, \u0000 \u0000where c(x,y,z)c(x,y,z) denotes the branch point generated by x,y,zx,y,z. If (T,r)(T,r) is a discrete tree, XX is a continuous time nearest neighbor random walk which jumps from vv to v′∼vv′∼v at rate 12⋅(ν({v})⋅r(v,v′))−112⋅(ν({v})⋅r(v,v′))−1. If (T,r)(T,r) is path-connected, XX has continuous paths and equals the νν-Brownian motion which was recently constructed in [Trans. Amer. Math. Soc. 365 (2013) 3115–3150]. In this paper, we show that speed-νnνn motions on (Tn,rn)(Tn,rn) converge weakly in path space to the speed-νν motion on (T,r)(T,r) provided that the underlying triples of metric measure spaces converge in the Gromov–Hausdorff-vague topology introduced in [Stochastic Process. Appl. 126 (2016) 2527–2553].","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/15-AOP1071","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66033248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 40

Strong uniqueness for SDEs in Hilbert spaces with nonregular drift 具有不规则漂移的Hilbert空间中SDEs的强唯一性

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-04-22 DOI: 10.1214/15-AOP1016

G. Prato, Franco Flandoli, M. Röckner, A. Veretennikov

引用次数: 46

Smooth approximation of stochastic differential equations 随机微分方程的光滑逼近

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-03-28 DOI: 10.1214/14-AOP979

David Kelly, I. Melbourne

{"title":"Smooth approximation of stochastic differential equations","authors":"David Kelly, I. Melbourne","doi":"10.1214/14-AOP979","DOIUrl":"https://doi.org/10.1214/14-AOP979","url":null,"abstract":"Consider an Ito process X satisfying the stochastic differential equation dX=a(X)dt+b(X)dW where a,b are smooth and W is a multidimensional Brownian motion. Suppose that Wn has smooth sample paths and that Wn converges weakly to W. A central question in stochastic analysis is to understand the limiting behavior of solutions Xn to the ordinary differential equation dXn=a(Xn)dt+b(Xn)dWn. \u0000The classical Wong–Zakai theorem gives sufficient conditions under which Xn \u0000converges weakly to X provided that the stochastic integral ∫b(X)dW is given the Stratonovich interpretation. The sufficient conditions are automatic in one dimension, but in higher dimensions the correct interpretation of ∫b(X)dW depends sensitively on how the smooth approximation Wnis chosen. \u0000In applications, a natural class of smooth approximations arise by setting Wn(t)=n−1/2∫nt0v∘ϕsds where ϕt is a flow (generated, e.g., by an ordinary differential equation) and v is a mean zero observable. Under mild conditions on ϕt, we give a definitive answer to the interpretation question for the stochastic integral ∫b(X)dW. Our theory applies to Anosov or Axiom A flows ϕt, as well as to a large class of nonuniformly hyperbolic flows (including the one defined by the well-known Lorenz equations) and our main results do not require any mixing assumptions on ϕt. \u0000The methods used in this paper are a combination of rough path theory and smooth ergodic theory.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/14-AOP979","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66010097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 90

cluster sets for partial sums and partial sum processes 部分和和过程的聚类集

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-03-27 DOI: 10.1214/12-AOP827

U. Einmahl, J. Kuelbs

{"title":"cluster sets for partial sums and partial sum processes","authors":"U. Einmahl, J. Kuelbs","doi":"10.1214/12-AOP827","DOIUrl":"https://doi.org/10.1214/12-AOP827","url":null,"abstract":"Let $X,X_1,X_2,ldots$ be i.i.d. mean zero random vectors with values in a separable Banach space $B$, $S_n=X_1+cdots+X_n$ for $nge1$, and assume ${c_n:nge1}$ is a suitably regular sequence of constants. Furthermore, let $S_{(n)}(t),0le tle1$ be the corresponding linearly interpolated partial sum processes. We study the cluster sets $A=C({S_n/c_n})$ and $mathcal{A}=C({S_{(n)}(cdot)/c_n})$. In particular, $A$ and $mathcal{A}$ are shown to be nonrandom, and we derive criteria when elements in $B$ and continuous functions $f:[0,1]to B$ belong to $A$ and $mathcal{A}$, respectively. When $B=mathbb{R}^d$ we refine our clustering criteria to show both $A$ and $mathcal{A}$ are compact, symmetric, and star-like, and also obtain both upper and lower bound sets for $mathcal{A}$. When the coordinates of $X$ in $mathbb{R}^d$ are independent random variables, we are able to represent $mathcal {A}$ in terms of $A$ and the classical Strassen set $mathcal{K}$, and, except for degenerate cases, show $mathcal{A}$ is strictly larger than the lower bound set whenever $dge2$. In addition, we show that for any compact, symmetric, star-like subset $A$ of $mathbb{R}^d$, there exists an $X$ such that the corresponding functional cluster set $mathcal{A}$ is always the lower bound subset. If $d=2$, then additional refinements identify $mathcal{A}$ as a subset of ${(x_1g_1,x_2g_2):(x_1,x_2)in A,g_1,g_2inmathcal{K}}$, which is the functional cluster set obtained when the coordinates are assumed to be independent.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/12-AOP827","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65971544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Systems of interacting diffusions with partial annihilation through membranes 通过膜的部分湮灭的相互作用扩散系统

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-03-24 DOI: 10.1214/15-AOP1047

Zhen-Qing Chen, W. Fan

引用次数: 8

From random lines to metric spaces 从随机线到度量空间

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-03-05 DOI: 10.1214/14-AOP935

W. Kendall

{"title":"From random lines to metric spaces","authors":"W. Kendall","doi":"10.1214/14-AOP935","DOIUrl":"https://doi.org/10.1214/14-AOP935","url":null,"abstract":"Consider an improper Poisson line process, marked by positive speeds so as to satisfy a scale-invariance property (actually, scale-equivariance). The line process can be characterized by its intensity measure, which belongs to a one-parameter family if scale and Euclidean invariance are required. This paper investigates a proposal by Aldous, namely that the line process could be used to produce a scale-invariant random spatial network (SIRSN) by means of connecting up points using paths which follow segments from the line process at the stipulated speeds. It is shown that this does indeed produce a scale-invariant network, under suitable conditions on the parameter; in fact, it then produces a parameter-dependent random geodesic metric for dd-dimensional space (d≥2d≥2), where geodesics are given by minimum-time paths. Moreover, in the planar case, it is shown that the resulting geodesic metric space has an almost everywhere unique-geodesic property that geodesics are locally of finite mean length, and that if an independent Poisson point process is connected up by such geodesics then the resulting network places finite length in each compact region. It is an open question whether the result is a SIRSN (in Aldous’ sense; so placing finite mean length in each compact region), but it may be called a pre-SIRSN.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2014-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/14-AOP935","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66007047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Characterization of positively correlated squared Gaussian processes 正相关平方高斯过程的表征

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-02-25 DOI: 10.1214/12-AOP807

Nathalie Eisenbaum

引用次数: 14

Quenched asymptotics for Brownian motion in generalized Gaussian potential 广义高斯势下布朗运动的淬灭渐近性

IF 2.3 1区数学

Annals of Probability Pub Date : 2014-02-25 DOI: 10.1214/12-AOP830

Xia Chen

引用次数: 41