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作者：Doney, RA; Maller, RA
作者单位：University of Manchester; Australian National University; Australian National University
摘要：We establish an integral test involving only the distribution of the increments of a random walk S which determines whether lim sup(n-->infinity() S-n/n(k)) is almost surely zero, finite or infinite when 1/2 < k < 1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now have quite explicit criteria for all values of k >= 0. The results, and those of [9], ...
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作者：Dedecker, J; Prieur, C
作者单位：Sorbonne Universite; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：To measure the dependence between a real-valued random variable X and a sigma-algebra M, we consider four distances between the conditional distribution function of X given M and the distribution function of X. The coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations. In particular, we show that they are well adapted to functions of mixing sequences, iterated random functions and dynamical systems. Starting from a new covariance ine...
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作者：Hamadène, S; Hassani, M
作者单位：Le Mans Universite
摘要：In this paper we show the existence of a solution for the BSDE with two reflecting barriers when those latter are completely separated. Neither Mokobodzki's condition nor the regularity of the barriers are supposed. The main tool is the notion of local solution of reflected BSDEs. Applications related to Dynkin games and double obstacle variational inequality are given.
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作者：Guionnet, A; Mazza, C
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Geneva
摘要：We consider the solution of a nonlinear Kraichnan equation partial derivative H-s(s, t) = integral(s)(t) H(s, u) H(u, t) k(s, u) du, s >= t with a covariance kernel k and boundary condition H( t, t) = 1. We study the long time behaviour of H as the time parameters t, s go to infinity, according to the asymptotic behaviour of k. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linea...
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作者：Krylov, NV; Röckner, M
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：We prove existence and uniqueness of strong solutions to stochastic equations in domains G subset of R-d with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local L-q-L-p-integrability of b in R x G with d/ p+ 2/ q < 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function psi blowing up as G there exists x --> partial derivativeG, we prove that the conditions 2D(t) psi less than or equal to Kpsi, 2D...
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作者：van der Hofstad, R; Sakai, A
作者单位：Eindhoven University of Technology
摘要：We consider self-avoiding walk and percolation in Z(d), oriented percolation in X-d x Z(+), and the contact process in Z(d), with pD(center dot) being the coupling function whose range is proportional to L. For percolation, for example, each bond is independently occupied with probability p D(y-x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical point p(c). We investigate the value of p(c) when d > 6 for percolation and d >...
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作者：Duquesne, T; Le Gall, JF
作者单位：Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We investigate the random continuous trees called Levy trees, which are obtained as scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted R-trees, which is equipped with the Gromov-Hausdorff distance. To construct Levy trees, we make use of the coding by the height process which was studied in detail in previous work. We then investigate various prob...
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作者：Clark, JMC; Crisan, D
作者单位：Imperial College London; Imperial College London
摘要：The paper is concerned with completing unfinished business on a robust representation formula for the conditional expectation operator of nonlinear filtering. Such a formula, robust in the sense that its dependence on the process of observations is continuous, was stated in [2] without proof. The main purpose of this paper is to repair this deficiency. The formula is almost obvious as it can be derived at a formal level by a process of integration-by-parts applied to the stochastic integrals t...
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作者：Rassoul-Agha, F; Seppalainen, T
作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L-2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic ...
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作者：Breuillard, E
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the speed of convergence of n(d/2) integral fd mu(*n) in the local limit theorem on R-d under very general conditions upon the function f and the distribution mu. We show that this speed is at least of order 1/n and we give a simple characterization (in diophantine terms) of those measures for which this speed (and the full local Edgeworth expansion) holds for smooth enough f. We then derive a uniform local limit theorem for moderate deviations under a mild moment assumption. This in ...
