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作者：Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13; Universite Paris Cite; Sorbonne Universite
摘要：We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609-631]. Our method applies, furthermore, to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of conv...
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作者：Addario-Berry, Louigi; Reed, Bruce
作者单位：Universite de Montreal; McGill University; Inria; Universite Cote d'Azur
摘要：Given a branching random walk, let M-n be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{vertical bar M-n - EMn vertical bar > x}, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89-108], our results fully characterize the possible behavior of EMn when the branching random walk has bounded branching and step size.
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作者：Arguin, Louis-Pierre; Aizenman, Michael
作者单位：Princeton University; Princeton University
摘要：We study point processes on the real line whose configurations X are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and quantified by a matrix Q = {q(ij)}(i,j is an element of N). A probability measure on the pair (X, Q) is said to be quasi-stationary if the joint law of the gaps of X and of Q is invariant under the evolution. A known class of universally quasi-stationary processes ...
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作者：Unterberger, Jeremie
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：The d-dimensional fractional Brownian motion (FBM for short) B(t) = ((B(t)((1)),...,B(t)((d))), t is an element of R) with Hurst exponent alpha, alpha is an element of (0, 1), is a d-dimensional centered, self-similar Gaussian process with covariance E[B(s)((i)) B(t)((j))] = 1/2 delta(i), j (vertical bar s vertical bar(2 alpha) + vertical bar t vertical bar(2 alpha) - vertical bar t -s vertical bar(2 alpha)). The long-standing problem of defining a stochastic integration with respect to FBM (a...
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作者：Yilmaz, Atilla
摘要：We consider random walk (X(n))(n >= 0) on Z(d) in a space-time product environment omega is an element of Omega. We take the point of view of the particle and focus on the environment Markov chain (T(n),X(n)omega)(n >= 0) where T denotes the shift on Omega. Conditioned on the particle having asymptotic mean velocity equal to any given xi, we show that the empirical process of the environment Markov chain converges to a stationary process mu(infinity)(xi) under the averaged measure. When d >= 3...
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作者：Angel, Omer; Holroyd, Alexander; Romik, Dan
作者单位：University of British Columbia; Microsoft; Hebrew University of Jerusalem
摘要：Particles labelled 1,..., n are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of rate 1. We analyze the asymptotic behavior of this process as n -> infinity. We prove that the space-time trajectories of individual particles converge (when suitably scaled) to a certain family of random curves with two points of non-differentiability, and that the permutation matrix at a given ti...
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作者：Zhang, Xicheng
作者单位：University of New South Wales Sydney; Huazhong University of Science & Technology
摘要：In this paper we first prove a Clark-Ocone formula for any bounded measurable functional on Poisson space. Then using this formula, under some conditions on the intensity measure of Poisson random measure, we prove a variational representation formula for the Laplace transform of bounded Poisson functionals, which has been conjectured by Dupuis and Ellis [A Weak Convergence Approach to the Theory of Large Deviations (1997) Wiley], p. 122.
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作者：Orsingher, Enzo; Beghin, Luisa
作者单位：Sapienza University Rome
摘要：In this paper the solutions u(nu) = u(nu) (x, t) to fractional diffusion equations of order 0 < v <= 2 are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations of order nu = 1/2(n), n >= 1, we show that the solutions u(1/2n) correspond to the distribution of the n-times iterated Brownian motion. For these processes the distributions of the maximum and of the sojourn time are explicitly given. The case of fractional equa...
