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作者：Gordon, Y; Litvak, A; Schütt, C; Werner, E
作者单位：Technion Israel Institute of Technology; University of Kiel; University System of Ohio; Case Western Reserve University
摘要：Let f(i), i = 1, n, be copies of a random variable f and let N be an Orlicz function. We show that for every x is an element of R-n the expectation Eparallel to(x(i)f(i))(i=1)(n)parallel to(N) is maximal (up to an absolute constant) if f(i), i = 1,...,n, are independent. In that case we show that the expectation Eparallel to(x(i) f(i))(i = 1)(n)parallel to(N) is equivalent to parallel toxparallel to(M), for some Orlicz function M depending on N and on distribution of f only. We provide applica...
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作者：Pra, PD; Paganoni, AM; Posta, G
作者单位：Polytechnic University of Milan
摘要：We consider nonconservative, reversible spin systems, with unbounded discrete spins. We show that for a class of these dynamics in a high temperature regime, the relative entropy with respect to the equilibrium distribution decays exponentially in time, although the logarithmic-Sobolev inequality fails. To this end we prove a weaker modification of the logarithmic-Sobolev inequality.
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作者：Dawson, DA; Etheridge, AM; Fleischmann, K; Mytnik, L; Perkins, EA; Xiong, J
作者单位：Carleton University; University of Oxford; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technion Israel Institute of Technology; University of British Columbia; University of Tennessee System; University of Tennessee Knoxville
摘要：We study a pair of populations in R-2 which undergo diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. For a diffusion rate sufficiently large compared with the branching rate, the model is constructed as the unique pair of finite measure-valued processes which satisfy a martingale problem involving the collision local time of the solutions. The processes are shown to have densities at fixed times w...
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作者：Scheutzow, M; Steinsaltz, D
作者单位：Technical University of Berlin; University of California System; University of California Berkeley
摘要：We consider the way sets are dispersed by the action of stochastic flows derived from martingale fields. Under fairly general continuity and ellipticity conditions, the following dichotomy result is shown: any nontrivial connected set X either contracts to a point under the action of the flow, or its diameter grows linearly in time, with speed at least a positive deterministic constant Lambda. The linear growth may further be identified (again, almost surely), with a much stronger behavior, wh...
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作者：Dawson, DA; Fleischmann, K; Mörters, P
作者单位：Carleton University; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Bath
摘要：A typical feature of the long time behavior of continuous super-Brownian motion in a stable catalytic medium is the development of large mass clumps (or clusters) at spatially rare sites. We describe this phenomenon by means of a functional limit theorem under renormalization. The limiting process is a Poisson point field of mass clumps with no spatial motion component and with infinite variance. The mass of each cluster evolves independently according to a non-Markovian continuous process tra...
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作者：Lalley, SP
作者单位：University of Chicago
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作者：Bossy, M; Jourdain, B
作者单位：Inria; Institut Polytechnique de Paris; Ecole des Ponts ParisTech
摘要：In this paper, we give a probabilistic interpretation of a viscous scalar conservation law in a bounded interval thanks to a nonlinear martingale problem. The underlying nonlinear stochastic process is reflected at the boundary to take into account the Dirichlet conditions. After proving uniqueness for the martingale problem, we show existence thanks to a propagation of chaos result. Indeed we exhibit a system of N interacting particles, the empirical measure of which converges to the unique s...
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作者：Borisov, IS; Ruzankin, PS
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics
摘要：Under minimal moment conditions complete asymptotic. expansions are obtained for expectations of unbounded functions of a finite family of independent random variables in the Poissonian setting when the distributions of the random variables have large atoms at zero.
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作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let {X-i; i greater than or equal to 1}, {Y-i; i > 1}, {U, U-i; i > 1} and {V, V-i; i greater than or equal to 1} be four i.i.d. sequences of random variables. Suppose U and V are uniformly distributed on [0, 1](3). For each realization of {U-j; 1 less than or equal to j less than or equal to n}, {X-i,X-p; 1 less than or equal to p less than or equal to n} is constructed as a certain permutation of {X-p; 1 less than or equal to p less than or equal to n} for any 1 less than or equal to i less ...
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作者：König, W; Mörters, P
作者单位：Technical University of Berlin; University of Bath
摘要：We equip the intersection of p independent Brownian paths in R-d, d greater than or equal to 2, with the natural measure l defined by projecting the intersection local time measure via one of the Brownian motions onto the set of intersection points. Given a bounded domain U subset of R-d we show that, as a up arrow infinity, the probability of the event {l(U) > a} decays with an exponential rate of a(1)/ptheta, where theta is described in terms of a variational problem. In the important specia...
