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作者：Kaufman, R; Wu, JM
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study bounded p-harmonic functions u defined on a directed tree T with branching order kappa (1 < p < infinity and kappa = 2, 3,...). Denote by BV(u) the set of paths on which u has finite variation and F(u) the set of paths on which rr has a finite limit. Then the infimum of dim BV(u) and the infimum of dim F(u) are equal over all bounded p-harmonic functions on T (with p and kappa fixed); the infimum d(kappa, p) is attained and is strictly between 0 and 1 expect when p = 2 or kappa = 2.
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作者：Gravner, J; Quastel, J
作者单位：University of California System; University of California Davis; University of Toronto
摘要：Generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as Poisson sources of particles which then perform symmetric random walks with an attractive zero-range interaction until they reach the first site which has been visited by fewer than a particles, at which point they stop. Sites on which particles are frozen constitute the occupied set. We prove that in appropriate regimes the particle density has a hydrodynamic...
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作者：Jeon, I; March, P; Pittel, B
作者单位：University System of Ohio; Ohio State University
摘要：We study the finite zero-range process with occupancy-dependent rate function g(.). Under the invariant measure, which can be written explicitly in terms of g, particles are distributed over sites and we regard all particles at a fixed site as a cluster. In the density one case, that; is, equal numbers of particles and sites, we determine asymptotically the size of the largest cluster, as the number of particles tends to infinity, and determine? its dependence on the rate function.
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作者：Mikulevicius, R
作者单位：Vilnius University
摘要：We study Cauchy's problem for certain second-order linear parabolic stochastic differential equation (SPDE) driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Holder classes.
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作者：Häggström, O; Schonmann, RH; Steif, JE
作者单位：Chalmers University of Technology; University of California System; University of California Los Angeles
摘要：Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. we show that for nonamenable graphs, for Bernoulli percolation with p close to 1, all the infinite clusters have persistent transition. On the other hand, we show that for transitive amenable graphs, the infinite clusters fbr any stationary percolation do not have persistent transition This extends a result of G...
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作者：O'Cinneide, C
作者单位：Purdue University System; Purdue University
摘要：We present a method for proving Perron-Frobenius eigenvalue inequalities. The method is to apply Jensen's inequality to the change in a random evolution over a regenerative cycle of the underlying finite-state Markov chain. One of the primary benefits of the method is that it readily gives necessary and sufficient conditions for strict inequality. It also gives insights into some of the conjectures of J. E. Cohen. Ney and Nummelin's Hypothesis 2 arises here as a condition for strict inequality...
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作者：Applebaum, D; Estrade, A
作者单位：Nottingham Trent University; Universite de Orleans
摘要：Under a natural invariance assumption on the Levy measure we construct compound Poisson processes and more general isotropic Levy processes on Riemannian manifolds by projection of a suitable horizontal process in the bundle of orthonormal frames. We characterize such Levy processes through their infinitesimal generators and we show that they can be realized as the limit of a sequence of Brownian motions which are interlaced with jumps along geodesic segments.
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作者：Latala, R; Zinn, J
作者单位：University of Warsaw; Texas A&M University System; Texas A&M University College Station
摘要：Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the strong law of large numbers for (symmetrized) U-statistics. We also obtain necessary and sufficient conditions for the a.s. convergence of series of an analogous form.
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作者：Kobylanski, M
作者单位：Universite de Tours
摘要：We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) F(t, Y, Z) is continuous and has a quadratic growth in Z and the terminal condition is bounded. We also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.
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作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; Lund University
摘要：Let Phi be a symmetric function, nondecreasing on [0, infinity) and satisfying a Delta (2) growth condition, (X-1, Y-1), (X-2, Y-2),...,(X-n, Y-n) be independent random vectors such that (for each 1 less than or equal to i less than or equal to n) either Y-i = X-i or Y-i is independent of all the other variates, and the marginal distributions of {X-i} and {Y-j} are otherwise arbitrary. Let {f(ij)(x, y)}(1 less than or equal toi, j less than or equal ton) be any array of real valued measurable ...
