2008

最新文章

• SPECTRAL GAPS IN WASSERSTEIN DISTANCES AND THE 2D STOCHASTIC NAVIER-STOKES EQUATIONS AI翻译
  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...
• A TREE APPROACH TO p-VARIATION AND TO INTEGRATION AI翻译
  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...
• Coincidence of Lyapunov exponents for random walks in weak random potentials AI翻译
  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.
• Exit from a basin of attraction for stochastic weakly damped nonlinear Schrodinger equations AI翻译
  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...
• Martingale dimensions for fractals AI翻译
  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].
• Large deviations AI翻译
  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.
• ON PATHWISE UNIQUENESS FOR REFLECTING BROWNIAN MOTION IN C1+γ DOMAINS AI翻译
  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.
• Large deviations for random walks under subexponentiality: The big-jump domain AI翻译
  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 ...
• Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials AI翻译
  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)........
• LP moduli of continuity of Gaussian processes and local times of symmetric Levy processes AI翻译
  作者：Marcus, Michael B.; Rosen, Jay
  作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
  摘要：Let X = {X(t), t epsilon R+} be a real-valued symmetric Levy process with local times {L-t(x), (t, X) epsilon R+ x R} and characteristic function e(i lambda X(t)) = et(-t psi(lambda)). Let sigma(2)(0)(x-y) = 4/pi integral(infinity)(0) sin(2)(lambda(x-y)/2)/psi(lambda) d lambda. If sigma(2)(0)(h) is concave, and satisfies some additional very weak regularity conditions, then for any p >= t and all t epsilon R+, lim(h down arrow 0)integral(b)(a)vertical bar L-t(x+h) - L-t(x)/sigma(0)(h)vertical ...