-
作者：Mountford, T; Sweet, T
作者单位：University of California System; University of California Los Angeles
摘要：Approximating a critical attractive reversible nearest particle system on a finite set from above is not difficult, but approximating it from below is less trivial, as the empty configuration is invariant. We develop a finite state Markov chain that deals with this issue. The rate of convergence for this chain is discovered through a mixing inequality in Jerrum and Sinclair; an application of that spectral gap bound in this case requires the use of randomized paths from state to state. For app...
-
作者：Cvitanic, J; Karatzas, I; Soner, HM
作者单位：Columbia University; Columbia University; Bogazici University
摘要：We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control-type equation. This representation is related to the pena...
-
作者：Grimmett, GR; Stacey, AM
作者单位：University of Cambridge
摘要：Any infinite graph G = (V, E) has a site percolation critical probability p(c)(site) and a bond percolation critical probability p(c)(bond). The well-known weak inequality p(c)(site) greater than or equal to p(c)(bond) is strengthened to strict inequality for a broad category of graphs G, including all the usual finite-dimensional lattices in two and more dimensions. The complementary inequality p(c)(site) less than or equal to 1 - (1 - p(c)(bond))(Delta - 1) is proved also, where Delta denote...
-
作者：Peskir, G
作者单位：Aarhus University; University of Zagreb
摘要：The solution is found to the optimal stopping problem with payoff sup(tau) E(S-tau - integral(0)(tau) c(Xt)dt), where S = (S-t)(t greater than or equal to 0) is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (X-t)(t greater than or equal to 0), the function x /--> c(x) is positive and continuous, and the supremum is taken over all stopping times tau of X for which the integral has finite expectation. It is proved, under no extra conditions, that this pro...
-
作者：Boué, M; Dupuis, P
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Brown University
摘要：In this paper we show that the variational representation -log Ee(-f(W)) = inf(v) E{1/2 integral(0)(1)//vs//(2) ds + f(W + integral(0)(.) vs ds)} holds, where W is a standard d-dimensional Brownian motion, f is any bounded measurable function that maps E([0,1]: R-d) into R and the infimum is over all processes v that are progressively measurable with respect to the augmentation of the filtration generated by FV. An application is made to a problem concerned with large deviations, and an extens...
-
作者：Atar, R
作者单位：Technion Israel Institute of Technology
摘要：The optimal nonlinear filtering problem for a diffusion process in a noncompact domain, observed in white noise, is considered. It is assumed that the process is ergodic, the diffusion coefficient is constant and the observation is linear. Using known bounds on the conditional density, it is shown that when the observation noise is sufficiently small, the filter is exponentially stable, and that the decay rate of the total variation distance between differently initialized filtering processes ...
-
作者：Zerner, MPW
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Assign to the lattice sizes z is an element of Z(d) i.i.d. random 2d-dimensional vectors (omega(z, z + e))(/e/ = 1) whose entries take values in the open unit interval and add up to one. Given a realization w of this environment, let (X-n)(n greater than or equal to 0) be a Markov chain on hd which, when at z, moves one step to its neighbor z + e with transition probability omega(z, z + e). We derive a large deviation principle for X-n/n by means of a result similar to the shape theorem of fir...
-
作者：de Acosta, A; Ney, P
作者单位：University System of Ohio; Case Western Reserve University; University of Wisconsin System; University of Wisconsin Madison
摘要：A universal large deviation lower bound is proved for sums of Banach space valued functions of an irreducible, general state space Markov chain. There are no restrictions on the functions (other than measurability).
-
作者：Comets, F; Menshikov, M; Popov, S
作者单位：Universite Paris Cite; Universidade de Sao Paulo
摘要：We study two typical examples of countable Markov chains in random environment using the Lyapunov functions method: random walk and random string in random environment. In each case we construct an explicit Lyapunov function. Investigating the behavior of this function, we get the classification for recurrence, transience, ergodicity. We obtain new results for random strings in random environment, though we simply review well-known results for random walks using our approach.
-
作者：Goldman, PA
作者单位：Universite Claude Bernard Lyon 1
摘要：In connection with a conjecture stated by D. G. Kendall in the forties, we describe the asymptotic behavior of the distribution function of the area of the planar Crofton cell. We deduce from this (in support of his conjecture) that expressed in terms of eigenvalues, the large Crofton cells are nearly circular. We obtain also the asymptotic behavior of the Laplace transform of the law of the perimeter of the convex hull of planar Brownian motion run until time 1. This last result implies that ...
