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The front location in branching Brownian motion with decay of mass 质量衰减分支布朗运动的前沿位置
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-11-01 DOI: 10.1214/16-AOP1148
L. Addario-Berry, S. Penington
{"title":"The front location in branching Brownian motion with decay of mass","authors":"L. Addario-Berry, S. Penington","doi":"10.1214/16-AOP1148","DOIUrl":"https://doi.org/10.1214/16-AOP1148","url":null,"abstract":"We augment standard branching Brownian motion by adding a competitive interaction between nearby particles. Informally, when particles are in competition, the local resources are insufficient to cover the energetic cost of motion, so the particles’ masses decay. In standard BBM, we may define the front displacement at time tt as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from Θ(1)Θ(1) to o(1)o(1). We show that one can find arbitrarily large times tt for which this occurs at a distance Θ(t1/3)Θ(t1/3) behind the front displacement for standard BBM.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"3752-3794"},"PeriodicalIF":2.3,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46509277","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: 7
A Clark–Ocone formula for temporal point processes and applications 时间点过程的Clark-Ocone公式及其应用
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-09-01 DOI: 10.1214/16-AOP1136
I. Flint, G. Torrisi
{"title":"A Clark–Ocone formula for temporal point processes and applications","authors":"I. Flint, G. Torrisi","doi":"10.1214/16-AOP1136","DOIUrl":"https://doi.org/10.1214/16-AOP1136","url":null,"abstract":"We provide a Clark–Ocone formula for square-integrable functionals of a general temporal point process satisfying only a mild moment condition, generalizing known results on the Poisson space. Some classical applications are given, namely a deviation bound and the construction of a hedging portfolio in a pure-jump market model. As a more modern application, we provide a bound on the total variation distance between two temporal point processes, improving in some sense a recent result in this direction.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"3266-3292"},"PeriodicalIF":2.3,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1136","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47283691","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: 3
The Feynman–Kac formula and Harnack inequality for degenerate diffusions 简并扩散的费曼-卡茨公式和哈纳克不等式
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-09-01 DOI: 10.1214/16-AOP1138
C. Epstein, C. Pop
{"title":"The Feynman–Kac formula and Harnack inequality for degenerate diffusions","authors":"C. Epstein, C. Pop","doi":"10.1214/16-AOP1138","DOIUrl":"https://doi.org/10.1214/16-AOP1138","url":null,"abstract":"We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in population genetics, the so-called generalized Kimura diffusion operators Epstein and Mazzeo [SIAM J. Math. Anal. 42 (2010) 568–608; Degenerate Diffusion Operators Arising in Population Biology (2013) Princeton University Press; Applied Mathematics Research Express (2016)]. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients and the proof of the scale-invariant Harnack inequality for nonnegative solutions to the Kimura parabolic equation. The stochastic representation of solutions that we establish is a considerable generalization of the classical results on Feynman–Kac formulas concerning the assumptions on the degeneracy of the diffusion matrix, the boundedness of the drift coefficients and the a priori regularity of the weak solutions.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"3336-3384"},"PeriodicalIF":2.3,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1138","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46532803","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
Permanental vectors with nonsymmetric kernels 具有非对称核的永久向量
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-07-03 DOI: 10.1214/15-AOP1008
Nathalie Eisenbaum
{"title":"Permanental vectors with nonsymmetric kernels","authors":"Nathalie Eisenbaum","doi":"10.1214/15-AOP1008","DOIUrl":"https://doi.org/10.1214/15-AOP1008","url":null,"abstract":"A permanental vector with a symmetric kernel and index 22 is a squared Gaussian vector. The definition of permanental vectors is a natural extension of the definition of squared Gaussian vectors to nonsymmetric kernels and to positive indexes. The only known permanental vectors either have a positive definite kernel or are infinitely divisible. Are there some others? We present a partial answer to this question.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"210-224"},"PeriodicalIF":2.3,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/15-AOP1008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49029704","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: 3
Functional central limit theorem for a class of negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows 一类由保守流产生的负相关重尾平稳无穷可分过程的泛函中心极限定理
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-07-01 DOI: 10.1214/16-AOP1107
Paul Jung, Takashi Owada, G. Samorodnitsky
{"title":"Functional central limit theorem for a class of negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows","authors":"Paul Jung, Takashi Owada, G. Samorodnitsky","doi":"10.1214/16-AOP1107","DOIUrl":"https://doi.org/10.1214/16-AOP1107","url":null,"abstract":"We prove a functional central limit theorem for partial sums of symmetric stationary long-range dependent heavy tailed infinitely divisible processes. The limiting stable process is particularly interesting due to its long memory which is quantified by a Mittag–Leffler process induced by an associated Harris chain, at the discrete-time level. Previous results in Owada and Samorodnitsky [Ann. Probab. 43 (2015) 240–285] dealt with positive dependence in the increment process, whereas this paper derives the functional limit theorems under negative dependence. The negative dependence is due to cancellations arising from Gaussian-type fluctuations of functionals of the associated Harris chain. The new types of limiting processes involve stable random measures, due to heavy tails, Mittag–Leffler processes, due to long memory, and Brownian motions, due to the Gaussian second order cancellations. Along the way, we prove a function central limit theorem for fluctuations of functionals of Harris chains which is of independent interest as it extends a result of Chen [Probab. Theory Related Fields 116 (2000) 89–123].","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"2087-2130"},"PeriodicalIF":2.3,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46921277","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: 5
Quadratic BSDE with $mathbb{L}^{2}$-terminal data: Krylov’s estimate, Itô–Krylov’s formula and existence results 具有$mathbb｛L｝^｛2｝$终端数据的二次BSDE：Krylov估计，It？–Krylov公式和存在性结果
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-07-01 DOI: 10.1214/16-AOP1115
K. Bahlali, M. Eddahbi, Y. Ouknine
{"title":"Quadratic BSDE with $mathbb{L}^{2}$-terminal data: Krylov’s estimate, Itô–Krylov’s formula and existence results","authors":"K. Bahlali, M. Eddahbi, Y. Ouknine","doi":"10.1214/16-AOP1115","DOIUrl":"https://doi.org/10.1214/16-AOP1115","url":null,"abstract":"We establish a Krylov-type estimate and an Ito–Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This allows us to prove various existence and uniqueness results for some classes of QBSDEs with a square integrable terminal condition and sometimes a merely measurable generator. It turns out that neither the existence of exponential moments of the terminal datum nor the continuity of the generator are necessary to the existence and/or uniqueness of solutions. We also establish a comparison theorem for solutions of a particular class of QBSDEs with measurable generator. As a byproduct, we obtain the existence of viscosity solutions for a particular class of quadratic partial differential equations (QPDEs) with a square integrable terminal datum.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"2377-2397"},"PeriodicalIF":2.3,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1115","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46997673","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: 19
Fundamental solutions of nonlocal Hörmander’s operators II 非局部Hörmander算子的基本解Ⅱ
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-05-01 DOI: 10.1214/16-AOP1102
Xicheng Zhang
{"title":"Fundamental solutions of nonlocal Hörmander’s operators II","authors":"Xicheng Zhang","doi":"10.1214/16-AOP1102","DOIUrl":"https://doi.org/10.1214/16-AOP1102","url":null,"abstract":"Consider the following nonlocal integro-differential operator: for α∈(0,2)α∈(0,2):L(α)σ,bf(x):=p.v.∫|z|<δf(x+σ(x)z)−f(x)|z|d+αdz+b(x)⋅∇f(x)+Lf(x),Lσ,b(α)f(x):=p.v.∫|z|<δf(x+σ(x)z)−f(x)|z|d+αdz+b(x)⋅∇f(x)+Lf(x),where σ:Rd→Rd⊗Rdσ:Rd→Rd⊗Rd and b:Rd→Rdb:Rd→Rd are smooth functions and have bounded partial derivatives of all orders greater than 11, δδ is a small positive number, p.v. stands for the Cauchy principal value and LL is a bounded linear operator in Sobolev spaces. Let B1(x):=σ(x)B1(x):=σ(x) and Bj+1(x):=b(x)⋅∇Bj(x)−∇b(x)⋅Bj(x)Bj+1(x):=b(x)⋅∇Bj(x)−∇b(x)⋅Bj(x) for j∈Nj∈N. Suppose Bj∈C∞b(Rd;Rd⊗Rd)Bj∈Cb∞(Rd;Rd⊗Rd) for each j∈Nj∈N. Under the following uniform Hormander’s type condition: for some j0∈Nj0∈N,infx∈Rdinf|u|=1∑j=1j0|uBj(x)|2>0,infx∈Rdinf|u|=1∑j=1j0|uBj(x)|2>0,by using Bismut’s approach to the Malliavin calculus with jumps, we prove the existence of fundamental solutions to operator L(α)σ,bLσ,b(α). In particular, we answer a question proposed by Nualart [Sankhyā A 73 (2011) 46–49] and Varadhan [Sankhyā A 73 (2011) 50–51].","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"1799-1841"},"PeriodicalIF":2.3,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42248381","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
Invariance principles under the Maxwell–Woodroofe condition in Banach spaces Banach空间中Maxwell-Woodroofe条件下的不变性原理
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-05-01 DOI: 10.1214/16-AOP1095
C. Cuny
{"title":"Invariance principles under the Maxwell–Woodroofe condition in Banach spaces","authors":"C. Cuny","doi":"10.1214/16-AOP1095","DOIUrl":"https://doi.org/10.1214/16-AOP1095","url":null,"abstract":"We prove that, for (adapted) stationary processes, the so-called Maxwell–Woodroofe condition is sufficient for the law of the iterated logarithm and that it is optimal in some sense. That result actually holds in the context of Banach valued stationary processes, including the case of $L^{p}$-valued random variables, with $1le p<infty$. In this setting, we also prove the weak invariance principle, hence generalizing a result of Peligrad and Utev [Ann. Probab. 33 (2005) 798–815]. The proofs make use of a new maximal inequality and of approximation by martingales, for which some of our results are also new.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"1578-1611"},"PeriodicalIF":2.3,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48762318","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
A structure theorem for poorly anticoncentrated polynomials of Gaussians and applications to the study of polynomial threshold functions Gaussians弱反凝聚多项式的一个结构定理及其在多项式阈值函数研究中的应用
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-05-01 DOI: 10.1214/16-AOP1097
D. Kane
{"title":"A structure theorem for poorly anticoncentrated polynomials of Gaussians and applications to the study of polynomial threshold functions","authors":"D. Kane","doi":"10.1214/16-AOP1097","DOIUrl":"https://doi.org/10.1214/16-AOP1097","url":null,"abstract":"We prove a structural result for degree-dd polynomials. In particular, we show that any degree-dd polynomial, pp can be approximated by another polynomial, p0p0, which can be decomposed as some function of polynomials q1,…,qmq1,…,qm with qiqi normalized and m=Od(1)m=Od(1), so that if XX is a Gaussian random variable, the probability distribution on (q1(X),…,qm(X))(q1(X),…,qm(X)) does not have too much mass in any small box. \u0000 \u0000Using this result, we prove improved versions of a number of results about polynomial threshold functions, including producing better pseudorandom generators, obtaining a better invariance principle, and proving improved bounds on noise sensitivity.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"1612-1679"},"PeriodicalIF":2.3,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/16-AOP1097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46250420","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: 3
Poly-adic filtrations, standardness, complementability and maximality 多元过滤、标准性、互补性和最大性
IF 2.3 1区 数学
Annals of Probability Pub Date : 2017-03-01 DOI: 10.1214/15-AOP1085
Christophe Leuridan
{"title":"Poly-adic filtrations, standardness, complementability and maximality","authors":"Christophe Leuridan","doi":"10.1214/15-AOP1085","DOIUrl":"https://doi.org/10.1214/15-AOP1085","url":null,"abstract":"Etant donn{e}e une filtration $(zc_n)_{n le 0}$ index{e}e par les entiers n{e}gatifs, nous introduisons la notion de compl{e}mentabilit{e} pour les filtrations incluses dans $(zc_n)_{n le 0}$. Dans le cas de filtrations poly-adiques, nous d{e}finissons aussi la notion de maximalit{e}, dont nous donnons plusieurs caract{e}risations. Lorsque $(zc_n)_{n le 0}$ est poly-adique, nous montrons que toute filtration compl{e}mentable par une filtration kolmogorovienne est maximale dans $(zc_n)_{n le 0}$. Nous montrons que la r{e}ciproque est fausse, mais qu'une r{e}ciproque partielle est vraie. Cette r{e}ciproque partielle {e}tend le th{e}or{e}me d'isomorphisme lacunaire de Vershik dans le cas des filtrations poly-adiques.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":"45 1","pages":"1218-1246"},"PeriodicalIF":2.3,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/15-AOP1085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44029705","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: 3
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