-
作者：Bentkus, V; Juozulynas, A; Paulauskas, V
作者单位：Vilnius University; Vilnius University
摘要：The standard normal distribution Phi on R-d satisfies Phi ((partial derivativeC)(epsilon)) less than or equal to c(d)epsilon, for all epsilon > 0 and for all convex subsets C subset of R-d, with a constant c(d) which depends on the dimension d only. Here partial derivativeC denotes the boundary of C, and (partial derivativeC)(epsilon) stands for the epsilon -neighborhood of partial derivativeC. Such bounds for the normal measure of convex shells are extensively used to estimate the accuracy of...
-
作者：Bruss, FT
作者单位：Universite Libre de Bruxelles
摘要：The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value. We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the in well-known asymptoti...
-
作者：Sudbury, A
摘要：We consider interacting particle systems on Z which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b, c, d, e. We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from airy finite occupied set. In particular: an IFS with rates a, b, c, d, e has a positive probability of survival if b > 4d + 6a, c + a greater than or e...
-
作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
作者单位：Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; Technion Israel Institute of Technology
摘要：Let F(x, r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in R-3. We prove that sup(\x\less than or equal to 1) F(x, r)/(r(2) \log r\) --> 16/pi(2) a.s. as r --> 0, thus solving a problem posed by Taylor in 1974. Furthermore, for any a epsilon (0, 16/pi(2)), the Hausdorff dimension of the set of thick points x for which lim sup(r-->0) F(x, r)/(r(2)\log r\) = a is almost surely 2 - a pi(2)/8; this is the correct scaling to obtain a nondegenerate m...
-
作者：Samson, PM
作者单位：Universite de Toulouse
摘要：We prove concentration inequalities for some classes of Markov chains and Phi-mixing processes, with constants independent of the size of the sample, that extend the inequalities for product measures of Talagrand. The method is based on information inequalities put forward by Marton in case of contracting Markov chains. Using a simple duality argument on entropy, our results also include the family of logarithmic Sobolev inequalities for convex functions. Applications to bounds on supremum of ...
-
作者：Mueller, C
作者单位：University of Rochester
摘要：Consider the stochastic partial differential equation u(t) = u(xx) + u(gamma)(W)over dot, where x epsilon I equivalent to [0, J], (W)over dot = (W)over dot(t, x) is 2-parameter white noise, and we assume that the initial function u(0, x) is nonnegative and not identically 0. We impose Dirichlet boundary conditions on u in the interval I. We say that u blows up in finite time, with positive probability, if there is a random time T < infinity such that P(lim(t up arrowT) sup(x) u( t, x) = infini...
-
作者：Merlevède, F; Peligrad, M
作者单位：Sorbonne Universite; University System of Ohio; University of Cincinnati
摘要：We prove a central limit theorem for strongly mixing sequences under a sharp sufficient condition which combines the rate of the strong mixing coefficient with the quantile function. The result improves on all earlier central limit theorems for this type of dependence and answers a conjecture raised by Bradley in 1997. Moreover, we derive the corresponding functional central limit theorem.
-
作者：Chen, X; Kuelbs, J; Li, WB
作者单位：Northwestern University; University of Wisconsin System; University of Wisconsin Madison; University of Delaware
摘要：A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion. Proofs depend on small ball probability estimates and yield the small ball probabilities of the weighted sup-norm for these processes.
-
作者：Cox, JT; Durrett, R; Perkins, EA
作者单位：Syracuse University; Cornell University; University of British Columbia
摘要：We show that a sequence of voter models, suitably rescaled in space and time, converges weakly to super-Brownian motion. The result includes both nearest neighbor and longer range voter models and complements a limit theorem of Mueller and Tribe in one dimension.
-
作者：Chiang, TS; Sheu, SJ
作者单位：Academia Sinica - Taiwan
摘要：where b is smooth except possibly along the hyperplane x(1) = 0, we shall consider the large deviation principle for the law of the solution diffusion process and its occupation time as epsilon --> 0. In other words, we consider P(\\X-epsilon - phi\\ < delta, \\u(epsilon) - psi\\ < delta) where u(epsilon)(t) and psi(t) are the occupation times of XE and cp in the positive half space {x epsilon R-d: x(1) > 0}, respectively. As a consequence, an unified approach of the lower level large deviatio...
