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作者：Liggett, Thomas M.; Steif, Jeffrey E.; Toth, Balint
作者单位：University of California System; University of California Los Angeles; Chalmers University of Technology; University of Gothenburg
摘要：We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie-Weiss Ising model and includes as well all ferromagnetic Curie-Weiss Potts and Curie-Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide ...
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作者：Gaertner, Juergen; Koenig, Wolfgang; Molchanov, Stanislav
作者单位：Technical University of Berlin; University of North Carolina; University of North Carolina Charlotte; Leipzig University
摘要：We consider the parabolic Anderson problem partial derivative(t)u = Delta u + xi(x)u on R+ x Z(d) with localized initial condition u (0, x) = delta(0)(x) and random i.i.d. potential xi. Under the assumption that the distribution of xi(0) has a double-exponential, or slightly heavier, tail, we prove the following geometric characterization of intermittency: with probability one, as t -> infinity, the over-whelming contribution to the total mass Sigma x u(t, x) comes from a slowly increasing num...
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作者：Talet, Marina
作者单位：Aix-Marseille Universite
摘要：We study Brownian motion in a drifted Brownian potential. Kawazu and Tanaka [J. Math. Soc. Japan 49 (1997) 189-211] exhibited two speed regimes for this process, depending on the drift. They supplemented these laws of large numbers by central limit theorems, which were recently completed by Hu, Shi and Yor [Trans. Amen Math. Soc. 351 (1999) 3915-3934] using stochastic calculus. We studied large deviations [Ann. Probab. 29 (2001) 11731204], showing among other results that the rate function in ...
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作者：Goldstein, Larry
作者单位：University of Southern California
摘要：The zero bias distribution W* of W, defined though the characterizing equation EW f (W) = sigma(2) Ef ''(W*) for all smooth functions f, exists for all W with mean zero and finite variance sigma(2). For W and W* defined on the same probability space, the L-1 distance between F, the distribution function of W with EW = 0 and Var(W) = 1, and the cumulative standard normal phi has the simple upper bound parallel to F - Phi parallel to(1) <= vertical bar W-* - W vertical bar This inequality is use...
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作者：Holmes, Mark; Perkins, Edwin
作者单位：Euratom; University of British Columbia
摘要：We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the r-point functions and perhaps convergence of the survival probabilities. These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical ...
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作者：Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna
作者单位：University of Warsaw; University of Warsaw
摘要：We prove a functional limit theorem for the resealed occupation time fluctuations of a (d, alpha, beta)-branching particle system [particles moving in R-d according to a symmetric alpha-stable Levy process, branching law in the domain of attraction of a (1+ beta)-stable law, 0 < beta < 1, uniform Poisson initial state] in the case of intermediate dimensions, alpha / beta < d < alpha (1+ beta) / beta. The limit is a process of the form K gimel xi, where K is a constant, gimel is the Lebesgue me...
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作者：Sezer, Deniz
作者单位：York University - Canada
摘要：We develop the mathematics of a filtration shrinkage model that has recently been considered in the credit risk modeling literature. Given a finite collection of points x(1) < ... < x(N) in R, the region indicator function R(x) assumes the value i if x is an element of (x(i - 1), x(i)]. We take F to be the filtration generated by (R(X-t))(t >= 0), where X is a diffusion with infinitesimal generator A. We prove a martingale representation theorem for F in terms of stochastic integrals with resp...
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作者：Coviello, Rosanna; Russo, Francesco
作者单位：Scuola Normale Superiore di Pisa; Universite Paris 13
摘要：In this paper we discuss existence and uniqueness for a one-dimensional time inhomogeneous stochastic differential equation directed by an F-semi-martingale M and a finite cubic variation process which has the structure Q + R, where Q is a finite quadratic variation process and R is strongly predictable in some technical sense: that condition implies, in particular, that R is weak Dirichlet, and it is fulfilled, for instance, when R is independent of M. The method is based on a transformation ...
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作者：Brydges, David; van der Hofstad, Remco; Koenig, Wolfgang
作者单位：University of British Columbia; Eindhoven University of Technology; Leipzig University
摘要：We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following directions: (1) we derive large deviation upper estimates for the normalized local times beyond the expon...
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作者：Shi, Zhan; Zindy, Olivier
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Sinai's walk is a recurrent one-dimensional nearest-neighbor random walk in random environment. It is known for a phenomenon of strong localization, namely, the walk spends almost all time at or near the bottom of deep valleys of the potential. Our main result shows a weakness of this localization phenomenon: with probability one, the zones where the walk stays for the most time can be far away from the sites where the walk spends the most time. In particular, this gives a negative answer to a...
