-
作者：SZNITMAN, AS
作者单位：New York University
摘要：We consider Brownian motion evolving among killing traps. We develop a technique of ''enlargement of obstacles.'' This technique allows us to replace given trap configurations by configurations of enlarged traps, when deriving upper estimates on the probability that Brownian motion survives. Applied in a context of random obstacles, this reduces the complexity of the description for the environment seen by Brownian motion. We apply the method to the case where traps are distributed according t...
-
作者：KHOSHNEVISAN, D
摘要：We present a Brownian embedding for a broad class of compensated compound Poisson processes. Applications of this method are discussed for a problem of level crossings, as well as Donsker's invariance type of principles. In particular, we give a central limit theorem for local times.
-
作者：JACKA, SD
摘要：Let X be a semimartingale, and S its Snell envelope. Under the assumption that X and S are continuous semimartingales in H-1, this article obtains a new, maximal, characterisation of S, and gives an application to the optimal stopping of functions of diffusions. We present a counterexample to the standard assertion that S is just ''a martingale on the go-region and X on the stop-region.''
-
作者：BAILLON, JB; CLEMENT, PH; GREVEN, A; DENHOLLANDER, F
作者单位：University of Gottingen; Delft University of Technology; Utrecht University
摘要：This paper considers an infinite system of particles on the integers Z that: (1) step to the right with a random delay, and (2) split or die along the way according to a random law depending on their position. The exponential growth rate of the particle density is computed in the long time limit in the form of a variational formula that can be solved explicitly. The result reveals two phase transitions associated with localization vs. delocalization and survival vs. extinction. In addition, th...
-
作者：BORELL, C
摘要：Consider a convex domain B in R(n) and denote by p(t, x, y) the transition probability density of Brownian motion in B killed at the boundary of B. The main result in this paper, in particular, shows that the function s ln s(n)p(s2, x, y), (s, x, y) is-an-element-of R+ x B2, is concave.
-
作者：PINSKY, RG
摘要：Let L generate a transient diffusion X(t) on R(d) and let D be an exterior domain. Let h be the smallest positive solution of Lh = 0 in D and h = 1 on partial derivative D. Define X(h)(t) to be the process X(t) conditioned to hit partial derivative D. By Doob's h-transform theory, X(h)(t) is also a Markov diffusion and its generator L(h) is defined by L(h)f = (1/h)L(hf). Letting tau(D) be the hitting time of partial derivative D, define the harmonic measure for X(h)(t) on partial derivative D ...
-
作者：SUN, JY
摘要：This paper gives a general two-term approximation for the tail probability of the maxima of a class of differentiable Gaussian random fields and illustrates its potential statistical applications.
-
作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：We develop new tools that enable us to extend the majorizing measure lower bound to a large class of infinitely divisible processes. We show (in a rigorous sense) that the complexity of these processes is dominated by the complexity of the positive infinitely divisible processes.
-
作者：MOGULSKII, AA
摘要：This PaPer strengthens and generalizes some theorems proved earlier by Lynch and Sethuraman on large deviations (LD) for random processes with independent increments.
-
作者：DINWOODIE, IH
摘要：Assume a sequence of probabilities {P(n)} has a large deviation rate function I. It is proved that I takes a form analogous to a convex conjugate. If I is also assumed convex, then I is a convex conjugate of an explicitly defined function psi. The results are applied to the empirical law of a Markov chain yielding universal bounds on I. Examples are given of Markov chains in which the empirical law has a large deviation rate strictly between the given bounds.
