-
作者：Castell, F
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We prove a homogenization result for system of semilinear parabolic PDEs of the type partial derivative(t)u(epsilon) = (1)/(2)e(2V(x/epsilon)) div (e(-2V(x/epsilon)) a(x/epsilon)delu(epsilon)) + h(x,u(epsilon), delu(epsilon)). where V and a are random ergodic fields. We extend to the random case, results of Buck-dahn, Hu & Peng [4] for periodic structures. The same method involving stability results is applied. Our main tool is an L-p estimate for the gradient of the solution of the auxiliary ...
-
作者：Wang, WM
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We further develop thr supersymmetric formalism initiated in [W1] (see also [SjW]). We obtain the optimal mean field bounds at the critical energy for Lyapunov exponents of random walks in random potentials in Z(d) at weak disorder. This extends some of the results in [W1].
-
作者：Cancrini, N; Martinelli, F
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR); Sapienza University Rome; University of L'Aquila; Roma Tre University
摘要：We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on Z(d) at inverse temperature beta. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any beta, with probability one, the spectral gap of the generator of the dynamics in a box of side L centered at the origin scales like L-2. Such an estimate is then used to prove a decay to equilibrium fo...
-
作者：Coffman, EG Jr; Lueker, GS; Spencer, J; Winkler, PM
作者单位：Columbia University; University of California System; University of California Irvine; New York University; Alcatel-Lucent; Lucent Technologies; AT&T
摘要：A random rectangle is the product of two independent random intervals, each being the interval between two random points drawn independently and uniformly from [0, 1]. We prove that the number C-n of items in a maximum cardinality disjoint subset of n random rectangles satisfies n(1/2)/K less than or equal to ECn less than or equal to Kn(1/2,) where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that,...
-
作者：Burdzy, K; Le Gall, JF
作者单位：University of Washington; University of Washington Seattle; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider super-Brownian motion whose historical paths reflect from each other. unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any gamma > 0, a typical increment of a reflecting historical path over a...
-
作者：Brown, H; Hobson, D; Rogers, LCG
作者单位：University of Bath
摘要：Let (M-t) be any martingale with M-0 = 0, an intermediate law M-1 similar to mu (1), and terminal law M-2 similar to mu (2), and let (M) over bar (2) = sup(0 less than or equal to1 less than or equal to2) M-t. In this paper we prove that there exists an upper bound, with respect to stochastic ordering of probability measures, on the law of (M) over bar (2). We construct, using excursion theory, a martingale which attains this maximum. Finally we apply this result to the robust hedging of a loo...
-
作者：Bogachev, VI; Röckner, M
作者单位：Lomonosov Moscow State University; University of Bielefeld
摘要：We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application, we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations ...
