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作者：Levin, DA; Pemantle, R; Peres, Y
作者单位：University of Connecticut; University of Wisconsin System; University of Wisconsin Madison; Hebrew University of Jerusalem; University of California System; University of California Berkeley
摘要：Suppose that a coin with bias 9 is tossed at renewal times of a renewal process, and a fair coin is tossed at all other times. Let we be the distribution of the observed sequence of coin tosses, and let u(n) denote the chance of a renewal at time n. Harris and Keane showed that if Sigma(n=1)(infinity) u(n)(2)=infinity, then u(theta) and u(0) are singular, while if Sigma(n=1)(infinity) u(n)(2) < infinity and theta is small enough, then u(theta) is absolutely continuous with respect to go. They ...
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作者：Pemantle, R; Stacey, AM
作者单位：University System of Ohio; Ohio State University; University of Cambridge
摘要：We show that the branching random walk on a Galton-Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton-Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded deg...
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作者：Dembo, A; Gandolfi, A; Kesten, H
作者单位：Stanford University; Stanford University; University of Rome Tor Vergata; Cornell University
摘要：Let {X-upsilon, upsilon epsilon Z(d)) be i.i.d. random variables, and S(xi) = Sigma (upsilon epsilon xi) X-upsilon be the weight of a lattice animal xi. Let N-n = max{S(xi) : /xi/ = n and xi contains the origin} and G(n) = max{S(xi) : xi subset of or equal to [-n, n](d)). We show that, regardless of the negative tail of the distribution of X-upsilon, if E(X-upsilon(+))(d) (log(+)(X-upsilon(+))(d+a) < +infinity or some a > 0, then first, lim(n) n(-1)N(n) = N exists, is finite and constant a.e.;...
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作者：Ma, ZM; Xiang, KN
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University; Universidade de Lisboa
摘要：We construct a continuous superprocess X on M(Rd) which is the unique weak Feller extension of the empirical process of consistent k-point motions generated by a family of differential operators. The process X differs from known Dawson-Watanabe type, Fleming-Viot type and Ornstein-Uhlenbeck type superprocesses. This new type of superprocess provides a connection between stochastic flows and measure-valued processes, and determines a stochastic coalescence which is similar to those of Smoluchow...
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作者：Allouba, H; Zheng, W
作者单位：Indiana University System; Indiana University Bloomington; East China Normal University; University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst
摘要：We introduce a class of interesting stochastic processes based on Brownian-time processes. These are obtained by taking Markov processes and replacing the time parameter with the modulus of Brownian motion. They generalize the iterated Brownian motion (IBM) of Burdzy and the Markov snake of Le Gall, and they introduce new interesting examples. After defining Brownian-time processes, we relate them to fourth order parabolic partial differential equations (PDE's). We then study their exit proble...
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作者：Rezakhanlou, F
作者单位：University of California System; University of California Berkeley
摘要：We continue our investigations on a class of growth models introduced in a previous paper. Given a nonnegative function upsilon: Z(d) --> Z with upsilon(0) = 0, we define the space of configurations F to consist of functions h: Zd Z such that h(i)-h(j) < upsilon(i-j) for all i, j is an element of Z(d). We then take two sequences of independent Poisson clocks (p(+/-) (i, t): i is an element of Z(d)) of rates lambda(+/-). We start with a possibly random configuration h is an element of Gamma. Th...
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作者：Taleb, M
作者单位：Universite Paris Cite
摘要：We derive a large deviation principle both quenched and annealed for a one-dimensional diffusion process in a drifted Brownian environment providing the continuous time analogue of what Comets, Gantert and Zeitouni recently establish for the random walk in random environment. A key-ingredient, Kotani's lemma, allows us to compute the corresponding rate functions. The results are more explicit than in the discrete-time setting.
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作者：Howard, CD; Newman, CM
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); New York University
摘要：The metric D-alpha(q, q ') on the set Q of particle locations of a homogeneous Poisson process on R-d, defined as the infimum of (Sigmai \q(i) - q(i+1)\ (alpha))(1/alpha) over sequences in Q starting with q and ending with q ' (where \ (.)\ denotes Euclidean distance) has nontrivial geodesics when alpha > 1. The cases 1 < alpha < infinity are the Euclidean first-passage percolation (FPP) models introduced earlier by the authors, while the geodesics in the case alpha = infinity are exactly the ...
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作者：Zegarlinski, B
作者单位：Imperial College London
摘要：We show that a strong mixing condition implies a Bakry-Bobkov-Ledoux inequality for a probability measure on infinite-dimensional space.
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作者：Brzezniak, Z; Peszat, S
作者单位：University of Hull; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：The existence of a martingale solution to 2-dimensional stochastic Euler equations is proved. The constructed solution is a limit as the viscosity converges to zero of a sequence of solutions to modified Navier-Stokes equations.
