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作者：DURRETT, R; SCHINAZI, R
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We show that in between the two critical values for the contact process on trees, there are infinitely many extremal nontranslation invariant stationary distributions. This conclusion is reminiscent of results of Grimmett and Newman for percolation on the product of a tree with the integers where there is an intermediate phase with infinitely many infinite clusters.
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作者：Burdzy, K; SanMartin, J
作者单位：Universidad de Chile
摘要：Suppose epsilon is an element of [0, 1] and let theta(epsilon)(t) = (1 - epsilon)root 2tln(2)t. Let L(t)(epsilon) denote the amount of local time spent by Brownian motion on the curve theta(epsilon)(s) before time t. If epsilon > 0, then lim sup(t-->infinity)L(t)(epsilon)/root 2tln(2)t = 2 epsilon + o(epsilon). For epsilon = 0, a nontrivial lim sup result is obtained when the normalizing function root 2tln(2)t is replaced by g(t) = root t/ln(2)tln(3)t.
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作者：DAWSON, DA; FLEISCHMANN, K; LI, Y; MUELLER, C
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Rochester
摘要：In a one-dimensional single point-catalytic continuous super-Brownian motion studied by Dawson and Fleischmann, the occupation density measure lambda(c) at the catalyst's position C is shown to be a singular (diffuse) random measure. The source of this qualitative new effect is the irregularity of the varying medium delta(c) describing the point catalyst. The proof is based on a probabilistic characterization of the law of the Palm canonical clusters chi appearing in the Levy-Khintchine repres...
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作者：Toth, B
摘要：The ''true'' self-avoiding walk with bond repulsion is a nearest neighbor random walk on Z, for which the probability of jumping along a bond of the lattice is proportional to exp(-g . number of previous jumps along that bond). First we prove a limit theorem for the distribution of the local time process of this walk. Using this result, later we prove a local limit theorem, as A --> infinity, for the distribution of A(-2/3)X theta s/A, where theta s/A is a random time distributed geometrically...
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作者：LIU, XJ
摘要：We consider infinite particle systems on a countable set S with two-particle exclusion-eating motion determined by a symmetric transition function p(x, y). This is, in a certain sense, a mixture of the exclusion process and the voter model. We discuss the dual process of this process and use the dual process to give a description of the set of invariant measures and to prove an ergodic theorem.
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作者：DEHEUVELS, P; MASON, DM
作者单位：University of Delaware
摘要：We prove that the set of points where exceptional oscillations of empirical and related processes occur infinitely often is a random fractal, and evaluate its Hausdorff dimension.
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作者：SZNITMAN, AS
摘要：We consider a Brownian motion in a Poissonian potential conditioned to reach a remote location. We shaw that for typical configurations the expectation of the time H to reach this goal grows at most linearly in the distance from the goal to the origin. In spite of the fact that H has no finite exponential moment, we derive three exponential estimates, one of which concerns the size of a natural lattice animal attached to the trajectory of the process up to the goal.
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作者：Aspandiiarov, S; LeGall, JF
摘要：We study certain classes of exceptional times of a linear Brownian motion (B-t, t greater than or equal to 0). In particular, we consider the set K- of all instants t is an element of [0, 1] such that the value B-t of the Brownian motion at time t is greater than its mean value over all intervals [s, t], s < t. We also study the subset K of K- of all instants t such that in addition B, is greater than the mean value of B over the intervals [t, s], t < s less than or equal to 1. We compute the ...
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作者：Evans, SN; Perkins, EA
作者单位：University of British Columbia
摘要：It is known from previous work of the authors that any square-integrable functional of a superprocess may be represented as a constant plus a stochastic integral against the associated orthogonal martingale measure. Here we give, for a large class of such functionals, an explicit description of the integrand that is analogous to Clark's formula for the representation of certain Brownian functionals. As a consequence, we develop a partial analogue of the Wiener chaos expansion in the superproce...
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作者：EINMAHL, U
摘要：In a recent paper by the author it has been shown that there exists a general law of the iterated logarithm (LIL) in Banach space, which contains the LIL of Ledoux and Talagrand and an LIL for infinite-dimensional random variables in the domain of attraction to a Gaussian law as special cases. We now investigate the corresponding cluster set problem, which we completely solve for random vectors in two-dimensional Euclidean space. Among other things, we show that all cluster sets arising from t...
