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作者：Dalang, RC; Frangos, NE
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Athens University of Economics & Business
摘要：We consider the wave equation in two spatial dimensions driven by space-time Gaussian noise that is white in time but has a nondegenerate spatial covariance. We give a necessary and sufficient integral condition on the covariance function of the noise for the solution to the linear form of the equation to be a real-valued stochastic process, rather than a distribution-valued random variable. When this condition is satisfied, we show that not only the linear form of the equation, but also nonli...
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作者：Grimmett, GR; Stacey, AM
作者单位：University of Cambridge
摘要：Any infinite graph G = (V, E) has a site percolation critical probability p(c)(site) and a bond percolation critical probability p(c)(bond). The well-known weak inequality p(c)(site) greater than or equal to p(c)(bond) is strengthened to strict inequality for a broad category of graphs G, including all the usual finite-dimensional lattices in two and more dimensions. The complementary inequality p(c)(site) less than or equal to 1 - (1 - p(c)(bond))(Delta - 1) is proved also, where Delta denote...
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作者：Peskir, G
作者单位：Aarhus University; University of Zagreb
摘要：The solution is found to the optimal stopping problem with payoff sup(tau) E(S-tau - integral(0)(tau) c(Xt)dt), where S = (S-t)(t greater than or equal to 0) is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (X-t)(t greater than or equal to 0), the function x /--> c(x) is positive and continuous, and the supremum is taken over all stopping times tau of X for which the integral has finite expectation. It is proved, under no extra conditions, that this pro...
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作者：Boué, M; Dupuis, P
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Brown University
摘要：In this paper we show that the variational representation -log Ee(-f(W)) = inf(v) E{1/2 integral(0)(1)//vs//(2) ds + f(W + integral(0)(.) vs ds)} holds, where W is a standard d-dimensional Brownian motion, f is any bounded measurable function that maps E([0,1]: R-d) into R and the infimum is over all processes v that are progressively measurable with respect to the augmentation of the filtration generated by FV. An application is made to a problem concerned with large deviations, and an extens...
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作者：Seppalainen, T
作者单位：Iowa State University
摘要：We study translation-invariant random-cluster measures with techniques from large deviation theory and convex analysis. In particular, we prove a large deviation principle with rate function given by a specific entropy, and a Dobrushin-Lanford-Ruelle variational principle that characterizes translation-invariant random-cluster measures as the solutions of the variational equation for free energy. Consequences of these theorems include inequalities for edge and cluster densities of translation-...
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作者：Berkes, I; Philipp, W
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We extend Levy's classical criterion for a sequence of independent identically distributed random variables to belong to the domain of partial attraction of a nondegenerate Gaussian law to stationary phi-mixing sequences. We also extend some results of Kesten and of Kuelbs and Zinn on the LIL behavior of independent identically distributed random variables to stationary phi-mixing sequences. No assumptions on the rate of decay for the mixing coefficient are made.
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作者：Duheille, F
作者单位：Universite Claude Bernard Lyon 1
摘要：We prove that, under some general assumptions, the range of any nonconstant harmonic morphism from a simply connected open set U in R-n to R-3, n > 3, cannot avoid three concurrent half-lines, which is an extension to Picard's little theorem. To this end, we will prove two results concerning the windings of Brownian motion around three concurrent half-lines in R-3 and the recurrence of some domains linked with the harmonic morphism.
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作者：Atar, R
作者单位：Technion Israel Institute of Technology
摘要：The optimal nonlinear filtering problem for a diffusion process in a noncompact domain, observed in white noise, is considered. It is assumed that the process is ergodic, the diffusion coefficient is constant and the observation is linear. Using known bounds on the conditional density, it is shown that when the observation noise is sufficiently small, the filter is exponentially stable, and that the decay rate of the total variation distance between differently initialized filtering processes ...
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作者：Cepa, E
作者单位：Universite de Orleans
摘要：An existence and uniqueness result is proven for a generalization (by introduction of a multivalued maximal monotone operator) of the deterministic Skorohod problem (with normal reflection) associated with a closed convex D in R-d. The maximal monotone operator formulation allows for drifts that blow up as one gets near the boundary. This multivalued approach clarifies the connection between nonlinear semigroup theory and the Skorohod problem. As a consequence, we discuss then the stochastic c...
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作者：Aaronson, J; Denker, M
作者单位：Tel Aviv University; University of Gottingen
摘要：The domain of attraction of a 1-stable law on R-d is characterized by the expansions of the characteristic functions of its elements.
