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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...
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作者：KALPAZIDOU, S
摘要：Let (S-i, i = 1, 2,..., n), n > 1, be a partition of the circle into sets S-i each consisting of union of delta(i) < infinity, arcs A(kl). Let f(t) be a rotation of length t of the circle and denote Lebesgue measure by lambda. Then every recurrent stochastic matrix P on S = {1,..., n} is given according to a theorem of Cohen (n = 2), Alpern and Kalpazidou (n greater than or equal to 2) by p(ij) = lambda S-i boolean AND f(t)(-1)(S-j))/lambda(Si) for some choice of rotation f(t) and partition L ...
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作者：LeGall, JF; Perkins, EA
作者单位：University of British Columbia
摘要：We show that two-dimensional super-Brownian motion is a multiple of the h-Hausdorff measure on its closed support, where h(r) = r(2) log(+)(1/r)log(+) log(+) log(+) (1/r). This complements known results in dimensions greater than 2.
