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作者：Pemantle, R; Peres, Y; Shapiro, JW
作者单位：University of California System; University of California Berkeley
摘要：We show that with probability 1, the trace B[0, 1] of Brownian motion in space, has positive capacity with respect to exactly the same kernels as the unit square. More precisely, the energy of occupation measure on B[0, 1] in the kernel f(\x - y\), is bounded above and below by constant multiples of the energy of Lebesgue measure on the unit square. (The constants are random, but do not depend on the kernel.) As an application, we give almost-sure asymptotics for the probability that an alpha-...
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作者：Fannjiang, A; Papanicolaou, G
作者单位：Stanford University
摘要：We prove long time diffusive behavior (homogenization) for convection-diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices.
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作者：Liverani, C; Olla, S
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Polytechnic University of Turin
摘要：We study the stationary measures of an infinite Hamiltonian system of interacting particles in R(3) subject to a stochastic local perturbation conserving energy and momentum. We prove that the translation invariant:measures that are stationary for the deterministic Hamiltonian dynamics, reversible for the stochastic dynamics, and with finite entropy density, are convex combination of ''Gibbs'' states. This result implies hydrodynamic behavior for the systems under consideration.
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作者：Schied, A
摘要：We derive two large deviation principles of Freidlin-Wentzell type for rescaled super-Brownian motion. For one of the appearing rate functions an integral representation is given and interpreted as 'Kakutani-Hellinger energy'. As a tool we develop estimates for the Laplace functionals of (historical) super-Brownian motion and certain maximal inequalities. Also it is shown that the Holder norm of index alpha < 1/2 of the process t --> (f,X(t)) possesses some finite exponential moments provided ...
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作者：Pitman, J
摘要：Local time processes parameterized by a circle, defined by the occupation density up to time T of Brownian motion with constant drift on the circle, are studied for various random times T. While such processes are typically non-Markovian, their Laplace functionals are expressed by series formulae related to similar formulae for the Markovian local time processes subject to the Ray-Knight theorems for BM on the line, and for squares of Bessel processes and their bridges. For T the time that BM ...
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作者：Thalmaier, A
摘要：We develop a general framework for a stochastic interpretation of certain nonlinear PDEs on manifolds. The linear operation of taking expectations is replaced by the concept of ''martingale means'', namely the notion of deterministic starting points of martingales (with respect to the Levi-Civita connection) ending up at a prescribed state. We formulate a monotonicity condition for the Riemannian quadratic variation of such martingales that allows us to turn smallness of the quadratic variatio...
