-
作者：Capinski, M; Cutland, NJ
作者单位：University of Hull
摘要：For 2-D stochastic Navier-Stokes equations on the torus with multiplicative noise we construct a perfect cocycle and show the existence of global random compact attractors. The equations considered do not admit a pathwise method of solution.
-
作者：Lahiri, SN
作者单位：Iowa State University
摘要：A spatial cumulative distribution function (F) over cap(infinity) (say) is a random distribution function that provides a statistical summary of random field over a given region. This paper considers the empirical predictor of (F) over cap(infinity) based on a finite set of observations from a region in R-d under a uniform sampling design. A functional central limit theorem is proved for the predictor as a random element of the space D[-infinity, infinity]. A striking feature of the result is ...
-
作者：Pisztora, A; Povel, T; Zeitouni, O
作者单位：Harvard University; Massachusetts Institute of Technology (MIT); Technion Israel Institute of Technology
摘要：Suppose that the integers are assigned i.i.d. random variables {w(x)} (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X-k} (called a RWRE) which, when at x, moves one step to the right with probability omega(x), and one step to the left with probability 1 - omega(x). Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlie...
-
作者：Bertini, L; Giacomin, G
作者单位：Sapienza University Rome; University of Zurich
摘要：We consider the stochastic heat equation in one space dimension and compute - for a particular choice of the initial datum - the exact long time asymptotic. In the Carmona-Molchanov approach to intermittence in non stationary random media this corresponds to the identification of the sample Lyapunov exponent, Equivalently, by interpreting the solution as the partition function of a directed polymer in a random environment, we obtain a weak law of large numbers for the quenched free energy. The...
-
作者：Anshelevich, M
作者单位：University of California System; University of California Berkeley
摘要：We interpret the Central Limit Theorem as a fixed point theorem for a certain operator, and consider the problem of linearizing this operator. In classical as well as in free probability theory [VDN92], we consider two methods giving such a linearization, and interpret the result as a weak form of the CLT. In the classical case the analysis involves dilation operators; in the free case more general composition operators appear. Mathematical Subject Classification (1991): Primary 46L50; Seconda...
-
作者：Pardoux, E; Tang, SJ
作者单位：Aix-Marseille Universite; Fudan University
摘要：This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate, continuous dependence on a parameter) of forward-backward stochastic differential equations and their connection with quasilinear parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward equation to be degenerate.
-
作者：Wentzell, AD
作者单位：Tulane University
摘要：For a certain class of families of stochastic processes eta(epsilon)(t), 0 less than or equal to t less than or equal to T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(eta(epsilon)[0, T]) are proved of the form EF(eta(epsilon)[0, T]) = E[F(omega(0)[0,T]) + (i=1)Sigma(m) epsilon(j/2) . A(i)F(omega(0)[0,T])] + o(epsilon(m/2)) (epsilon down arrow 0), where omega(0) is a Wiener process starting from 0, with variance sigma(2) per ...
-
作者：Gentz, B; Löwe, M
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bielefeld
摘要：We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1/beta(c), = 1, At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it is not given by a Dirac measure concentrated in a Gaussian di...
-
作者：Chaumont, L; Doney, RA
作者单位：Sorbonne Universite; University of Manchester
摘要：Any solution of the functional equation [GRAPHICS] where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an alpha-perturbed reflected Brownian motion. Similarly any solution of [GRAPHICS] behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an alpha,beta-doubly perturbed Brownian motion. We complete some recent investigations by showing that for all permissible values of the parameters alph...
-
作者：Häggström, O; Peres, Y
作者单位：Chalmers University of Technology; University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：Consider site or bond percolation with retention parameter p on an infinite Cayley graph. In response to questions raised by Grimmett and Newman (1990) and Benjamini and Schramm (1996), we show that the property of having (almost surely) a unique infinite open cluster is increasing in p. Moreover, in the standard coupling of the percolation models for all parameters, a.s. for all p(2) > p(1) > p(c), each infinite p(2)-cluster contains an infinite pr-cluster; this yields an extension of Alexand...
