4期

最新文章

• Asymptotic shapes for stationary first passage percolation AI翻译
  作者：Haggstrom, O; Meester, R
  作者单位：Utrecht University
  摘要：This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set B subset of R(d) to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.
• Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering AI翻译
  作者：Bhatt, AG; Kallianpur, G; Karandikar, RL
  作者单位：University of North Carolina; University of North Carolina Chapel Hill
  摘要：We consider the Zakai equation for the unnormalized conditional distribution sigma when the signal process X takes values in a complete separable metric space E and when h is a continuous, possibly unbounded function on E. It is assumed that X is a Markov process which is characterized via a martingale problem for an operator A(0). Uniqueness of solution for the measure-valued Zakai and Fujisaki-Kallianpur-Kunita equations is proved when the test functions belong to the domain of A(0). It is a...
• Geometric and symmetry properties of a nondegenerate diffusion process AI翻译
  作者：deLara, MC
  摘要：A diffusion process with smooth and nondegenerate elliptic infinitesimal generator on a manifold M induces a Riemannian metric g on M. This paper discusses in detail different symmetry properties of such a diffusion by geometric methods. Partial differential equations associated with the generator are studied likewise. With an eye to modelling and applications to filtering, relationships between symmetries of deterministic systems and symmetries of diffusion processes are delineated. The incid...
• The support of measure-valued branching processes in a random environment AI翻译
  作者：Dawson, D; Li, Y; Mueller, C
  作者单位：University of Rochester
  摘要：We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super-Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On t...
• Iterated law of iterated logarithm AI翻译
  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.
• The ''true'' self-avoiding walk with bond repulsion on Z: Limit theorems AI翻译
  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...
• Some new classes of exceptional times of linear Brownian motion AI翻译
  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 ...
• Explicit stochastic integral representations for historical functionals AI翻译
  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...
• The Hausdorff measure of the support of two-dimensional super-Brownian motion AI翻译
  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.
• Hydrodynamic scaling limits with deterministic initial configurations AI翻译
  作者：Lu, SL
  作者单位：University of Michigan System; University of Michigan
  摘要：We discuss the hydrodynamic scaling limits starting with deterministic configurations for different models. Certain estimates on the entropy of the system are derived.