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作者：Hairer, M
作者单位：University of Warwick
摘要：We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H is an element of (0, 1). A general framework is constructed to make precise the notions of invariant measure and stationary state for such a system. We then prove under rather weak dissipativity conditions that such an SIDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the statio...
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作者：Haydn, N; Lacroix, Y; Vaienti, S
作者单位：University of Southern California; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite
摘要：Given an ergodic dynamical system (X, T, mu), and U subset of X measurable with mu(U) > 0, let mu(U)tau(U)(x) denote the normalized hitting time of x is an element of X to U. We prove that given a sequence (U-n) with mu(U-n) -> 0, the distribution function of the normalized hitting times to U-n converges weakly to some subprobability distribution F if and only if the distribution function of the normalized return time converges weakly to some distribution function and that in the converging ca...
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作者：Xia, C
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let S-1 (n), . . ., S-p(n) be independent symmetric random walks in Z(d). We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S-1[0, n] boolean AND . . . boolean AND S-p[0, n]} in the case d = 2, p >= 2 and the case d = 3, p = 2.
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作者：Schramm, O; Sheffield, S
作者单位：Microsoft; University of California System; University of California Berkeley
摘要：The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.
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作者：Dubédat, J
作者单位：Universite Paris Saclay
摘要：Various features of the two-parameter family of Schramm-Loewner evolutions SLE(kappa, rho) are studied. In particular, we derive certain restriction properties that lead to a strong duality conjecture, which is an identity in law between the outer boundary of a variant of the SLE(kappa) process for kappa greater than or equal to 4 and a variant of the SLE(16/kappa) process.
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作者：DeBlassie, D
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：For continuous gamma, g:[0, 1] --> (0, infinity), consider the degenerate stochastic differential equation dX(t) = [1 - \X-t \(2)](1/2)gamma(\X-t\)dB(t) - g(\X-t\)X-t dt in the closed unit ball of R-n. We introduce a new idea to show pathwise uniqueness holds when gamma and g are Lipschitz and g(1)/gamma(2)(1) > root2 -1 . When specialized to a case studied by Swart [Stochastic Process. Appl. 98 (2002) 131-149] with gamma = root2 and g equivalent to c, this gives an improvement of his result. ...
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作者：Hassairi, A; Zarai, M
作者单位：Universite de Sfax; Faculty of Sciences Sfax
摘要：This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac-Mora characterization of the real natural exponential families having cubic variance function.
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作者：Asselah, A; Pra, PD
作者单位：Aix-Marseille Universite; University of Padua
摘要：We consider the symmetric exclusion process {eta(t), t > 0} on {0,1}(Zd). We fix a pattern A := {eta: Sigma(Lambda) eta(i) greater than or equal to k}, where Lambda is a finite subset of Z(d) and k is an integer, and we consider the problem of establishing sharp estimates for tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for tau in a simple way. Also, we characterize the trajectories {eta(s), s less than...
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作者：Dalang, RC; Nualart, E
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135-1159], where estimates for the hitting probabilities of the (N, d) Brownian sheet in terms of the (d - 2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, ...
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作者：De La Peña, VH; Klass, MJ; Lai, TL
作者单位：Columbia University; University of California System; University of California Berkeley; Stanford University
摘要：Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. Tail probability bounds are also derived. For random variables B-t > 0 and A(t), let Y-t(lambda) = ex...
