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作者：Chen, Zhen-Qing; Fitzsimmons, Patrick J.; Kuwae, Kazuhiro; Zhang, Tu-Sheng
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California San Diego; Kumamoto University; University of Manchester
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作者：Pardoux, Etienne; Piatnitski, Andrey
作者单位：Aix-Marseille Universite; UiT The Arctic University of Tromso
摘要：In this paper we study the homogenization of a nonautonomous parabolic equation with a large random rapidly oscillating potential in the case of one-dimensional spatial variable. We show that if the potential is a statistically homogeneous rapidly oscillating function of both temporal and spatial variables, then, under proper mixing assumptions, the limit equation is deterministic, and convergence in probability holds. To the contrary, for the potential having a microstructure only in one of t...
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作者：Privault, Nicolas
作者单位：Nanyang Technological University
摘要：We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals.
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作者：Roy, Emmanuel
作者单位：Universite Paris Cite
摘要：We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Levy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.
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作者：Keller, Nathan; Mossel, Elchanan; Sen, Arnab
作者单位：Weizmann Institute of Science; University of California System; University of California Berkeley; University of Cambridge
摘要：We present a new definition of influences in product spaces of continuous distributions. Our definition is geometric, and for monotone sets it is identical with the measure of the boundary with respect to uniform enlargement. We prove analogs of the Kahn-Kalai-Linial (KKL) and Talagrand's influence sum bounds for the new definition. We further prove an analog of a result of Friedgut showing that sets with small influence sum are essentially determined by a small number of coordinates. In parti...
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作者：Abraham, Romain; Delmas, Jean-Francois
作者单位：Universite de Orleans; Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：We present a construction of a Levy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov theorem. We also extend the pruning procedure to this super-critical case. Let psi be a critical branching mechanism. We set psi(theta)(.) = psi(. + theta) - psi(theta). Let Theta = (theta(infinity), +infinity) or Theta = [theta(infinity), +infinity) be the set of values of theta for which psi(theta) is a cons...
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作者：Ding, Jian; Lubetzky, Eyal; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 be the largest component of the Erdos-Renyi random graph G(n, p). The mixing time of random walk on C-1 in the strictly supercritical regime, p = c/n with fixed c > 1, was shown to have order log(2) n by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald. In the critical window, p = (1 + epsilon)/n where lambda = epsilon(3)n is bounded, Nachmias and Peres proved that the mixing time on C-1 is of order n. However, it was unclear how to interpolate between these res...
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作者：Letac, Gerard; Piccioni, Mauro
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sapienza University Rome
摘要：In a recent paper [Statist. Probab. Lett. 78 (2008) 1711-1721] it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function F-2(1). In the present paper we fully exploit a formula due to Thomae [J. Reine Angew. Math. 87 (1879) 26-73] in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on th...
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作者：Liu, Jingchen
作者单位：Columbia University
摘要：This paper develops asymptotic approximations of P(f(T) e(f(t)) dt > b) as b -> infinity for a homogeneous smooth Gaussian random field, f, living on a compact d-dimensional Jordan measurable set T. The integral of an exponent of a Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability P(f(Xi) e(f(t)) dt > b) over...
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作者：Grigor'yan, Alexander; Telcs, Andras
作者单位：University of Bielefeld; Budapest University of Technology & Economics
摘要：We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.
