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作者：Sun, Rongfeng; Swart, Jan M.
作者单位：Technical University of Berlin
摘要：The (standard) Brownian web is a collection of coalescing one-dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.
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作者：Hairer, Martin; Mattingly, Jonathan C.
作者单位：University of Warwick; Duke University
摘要：We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for this analysis is neither a weighted supremum norm nor an LP-type norm, but involves the derivative of the observable as well and hence can be seen as a type of 1-Wasserstein distance. This turns Out to be a suitable approach for infinite-dimensional spaces where the usual Harris or Doeblin conditions, which are geared toward tot...
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作者：Picard, Jean
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
摘要：We consider a real-valued path; it is possible to associate a tree to this path. and we explore the relations between the tree. the properties of p-variation of the path. and integration with respect to the path. In particular. the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include sortie stochastic paths such as marting...
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作者：Flury, Markus
作者单位：University of Zurich
摘要：We investigate the free energy of nearest-neighbor random walks on Z(d), endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions d >= 4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.
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作者：Gautier, Eric
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider weakly damped nonlinear Schrodinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically stable equilibrium point of the deterministic equations. We study the exit from a neighborhood of zero, invariant under the flow of the deterministic equation, in L-2 or in H-1. Due to noise, large fluctuations from zero occur. Thus, on a s...
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作者：Hino, Masanori
作者单位：Kyoto University
摘要：We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math. Sci. 25 (1989) 659-680].
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作者：Varadhan, S. R. S.
作者单位：New York University
摘要：This paper is based oil Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.
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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Pathwise uniqueness holds for the Skorokhod stochastic differential equation in C1+gamma domains in R-d for gamma > 1/2 and d >= 3.
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作者：Denisov, D.; Dieker, A. B.; Shneer, V.
作者单位：Heriot Watt University; International Business Machines (IBM); IBM USA; Euratom
摘要：For a given one-dimensional random walk {S-n} with a subexponential step-size distribution, we present a unifying theory to study the sequences {x(n)} for which P{S-n > x} as n -> infinity uniformly for x >= x(n). We also investigate the stronger local analogue, P{S-n is an element of (x, x + T]} similar to nP{S-1 is an element of (x, x + T]}. Out- theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the ...
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作者：Kim, Panki; Song, Renming
作者单位：Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：Recently, in [Preprint (2006)], we extended the concept of intrinsic ultra-contractivity to nonsymmetric semigroups. In this paper, we study the intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and measure-valued potentials in bounded domains. Our process Y is a diffusion process whose generator can be formally written as L + mu . del - v with Dirichlet boundary conditions, where L is a uniformly elliptic second-order differential operator and mu = (mu(l)........
