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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：Pipiras, V; Taqqu, MS
作者单位：Boston University
摘要：Let alpha is an element of (1, 2) and X-alpha be a symmetric alpha-stable (SalphaS) process with stationary increments given by the mixed moving average X-alpha(t) = integral(X) integral(R) (G(x, t + u) - G(x, u)) Malpha(dx, du), t is an element of R, where (X, chi, mu) is a standard Lebesgue space, G: X x R --> R is some measurable function and M-alpha is a SalphaS random measure on X x R with the control measure m(dx, du) = mu(dx)du. Assume, in addition, that X-alpha is self-similar with exp...
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作者：Kaimanovich, VA; Woess, W
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Graz University of Technology
摘要：We study the Poisson boundary (equivalent to representation of bounded harmonic functions) of Markov operators on discrete state spaces that are invariant under the action of a transitive group of permutations. This automorphism group is locally compact, but not necessarily discrete or unimodular. The main technical tool is the entropy theory which we develop along the same lines as in the case of random walks on countable groups, while, however, the implementation is different and exploits di...
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作者：Engelbert, HJ
作者单位：Friedrich Schiller University of Jena
摘要：We consider the one-dimensional stochastic equation X-t = X-0 + integral(0)(t) b(X-s) dM(s) where M is a continuous local martingale and b a measurable real function. Suppose that b(-2) is locally integrable. D. N. Hoover asserted that, on a saturated probability space, there exists a solution X of the above equation with X-0 = 0 having no occupation time in the zeros of b and, moreover, the pair (X, M) is unique in law for all such X. We will give an example which shows that the uniqueness as...
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作者：Fontes, LRG; Isopi, M; Newman, CM
作者单位：Universidade de Sao Paulo; Universita degli Studi di Bari Aldo Moro; New York University
摘要：Let tau = (tau(i) : i is an element of Z) denote i.i.d. positive random variables with common distribution F and (conditional on tau) let X = (X-t : t greater than or equal to 0, X-0 = 0), be a continuous-time simple symmetric random walk on Z with inhomogeneous rates (tau(i)(-1) : i is an element of Z). When F is in the domain of attraction of a stable law of exponent alpha < 1 [so that E(tau(i)) = infinity and X is subdiffusive], we prove that (X, tau), suitably rescaled (in space and time),...
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作者：Landim, C; Olla, S; Varadhan, SRS
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CY Cergy Paris Universite; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; New York University
摘要：We show that for the symmetric simple exclusion process on Z(d) the self-diffusion coefficient of a tagged particle is stable when approximated by simple exclusion processes on large periodic lattices. The proof depends on a similar stability property of the asymptotic variance of additive functionals of mean 0. This requires establishing a property for the Dirichlet space known as the Liouville-D property.
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作者：Fannjiang, AC; Komorowski, T
作者单位：Maria Curie-Sklodowska University; University of California System; University of California Davis
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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
