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作者：van den Berg, M; Bolthausen, E; den Hollander, F
作者单位：University of Bristol; University of Zurich
摘要：In this paper we consider a standard Brownian motion in R-d, starting at 0 and observed until time t. The Brownian motion takes place in the presence of a Poisson random field of traps, whose centers have intensity nu(t) and whose shapes are drawn randomly and independently according to a probability distribution Pi, on the set of closed subsets of R-d, subject to appropriate conditions. The Brownian motion is killed as soon as it hits one of the traps. With the help of a large deviation techn...
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作者：Franke, B
作者单位：Ruhr University Bochum; National Cheng Kung University
摘要：We prove a functional central limit theorem for diffusions on periodic sub- manifolds of R-N. The proof is an adaptation of a method presented in [BenLioPap] and [Bha] for proving functional central limit theorems for diffusions with periodic drift vectorfields. We then apply the central limit theorem in order to obtain a recurrence and a transience criterion for periodic diffusions. Other fields of applications could be heat-kernel estimates, similar to the ones obtained in [Lot].
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作者：Barndorff-Nielsen, OE; Thorbjornsen, S
作者单位：Aarhus University; University of Southern Denmark
摘要：In this paper we prove the free analog of the Levy-Ito decomposition for Levy processes. A significant part of the proof consists of introducing free Poisson random measures, proving their existence and developing a theory of integration with respect to such measures. The existence of free Poisson random measures also yields, via the free Levy-Ito decomposition, an alternative proof of the general existence of free Levy processes ( in law).
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作者：Kempe, J
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its st...
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作者：Petz, D; Réffy, J
作者单位：Budapest University of Technology & Economics
摘要：Let U-m be an mxm Haar unitary matrix and U-[m,U-n] be its nxn truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U-[m,U-n] as m/n -> lambda and n -> infinity. The rate function and the limit distribution are given explicitly. U-[m,U-n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.
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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：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：Mayer-Wolf, E; Zakai, M
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：The domain of definition of the divergence operator delta on an abstract Wiener space (W, H, mu) is extended to include W - valued and W x W - valued integrands. The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in delta' s extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by W-valued vector fields and, among other results, it turns out that these diver...
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作者：Ossiander, M
作者单位：Oregon State University
摘要：A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in R-3 with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations of functionals of a Markov process indexed by the nodes of a binary tree. It gives existence and uniqueness of weak solutions for all time under relatively simple conditions on the forcing and initial data. These conditions involve comparison of the forcing and initi...
