-
作者：Shirai, T; Takahashi, Y
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology; Kanazawa University; Kyoto University
摘要：We construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants. Under a mild condition they turn out unique Gibbs measures. Also some ergodic properties, including the entropy positivity, are discussed in the lattice case.
-
作者：Pardoux, É; Veretennikov, Y
作者单位：Aix-Marseille Universite; University of Leeds; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of an invariant diffusion density with respect to a parameter. The second establishes a similar smoothness of the solution of the Poisson equation in R-d. The third one states a diffusion approximation result, or in other words an averaging of singularly perturbed diffusion for fully coupled SDE syst...
-
作者：Bendikov, A; Saloff-Coste, L
作者单位：Cornell University
摘要：We study the regularity of the sample paths of certain Brownian motions on the infinite dimensional torus T-infinity and other compact connected groups in terms of the associated intrinsic distance. For each lambda is an element of (0, 1), we give examples where the intrinsic distance d is continuous and defines the topology of T-infinity and where the sample paths satisfy 0 < lim inf(t-->0) d(X-0,X-t)/t((1-lambda)/2) less than or equal to lim sup(t-->0) d(X-0,X-t)/t((1-lambda)/2) < infinity a...
-
作者：Jacka, S; Tribe, R
作者单位：University of Warwick
摘要：This paper considers some measure-valued processes {X-t:t is an element of [0, T]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Phi of the process are given that imply that the expectations E(Phi(X-T)) are comparable to the constant branching case. Applications to hitting estimates and regularity of solutions are discussed. The resul...
-
作者：Csörgö, M; Szyszkowicz, B; Wang, QY
作者单位：Carleton University; Australian National University
摘要：Let X, X-1, X-2,... be a sequence of nondegenerate i.i.d. random variables with zero means. In this paper we show that a self-normalized version of Donsker's theorem holds only under the assumption that X belongs to the domain of attraction of the normal law. A thus resulting extension of the arc sine law is also discussed. We also establish that a weak invariance principle holds true for self-normalized, self-randomized partial sums processes of independent random variables that are assumed t...
-
作者：Marckert, JF; Mokkadem, A
作者单位：Universite Paris Saclay
摘要：In this paper, we show a strong relation between the depth first processes associated to Galton-Watson trees with finite variance, conditioned by the total progeny: the depth first walk, the depth first queue process, the height process; a consequence is that these processes (suitably normalized) converge to the same Brownian excursion. This provides an alternative proof of Aldous' one of the convergence of the depth first walk to the Brownian excursion which does not use the existence of a li...
-
作者：Erschler, A
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：In this paper we consider drift and entropy growth for symmetric finitary random walks on finitely generated groups. We construct examples of various intermediate asymptotics of the drift for such random walks. We establish general inequalities which connect drift, entropy and exponential growth rate of groups. Then we apply these inequalities to get estimates for entropy in particular examples.
-
作者：Grothaus, M; Kondratiev, YG; Lytvynov, E; Röckner, M
作者单位：University of Bielefeld; University of Bonn; University of Bielefeld; National Academy of Sciences Ukraine; Institute of Mathematics of NASU
摘要：We investigate a scaling limit of gradient Stochastic dynamics associated with Gibbs states in classical continuous systems on R-d, d greater than or equal to 1. The aim is to derive macroscopic quantities from a given microscopic or mesoscopic system. The scaling we consider has been investigated by Brox (in 1980), Rost (in 1981), Spohn (in 1986) and Guo and Papanicolaou (in 1985), under the assumption that the underlying potential is in C-0(3) and positive. We prove that the Dirichlet forms ...
-
作者：Rassoul-Agha, F
作者单位：University System of Ohio; Ohio State University
摘要：The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or higher-dimensional, finite range, transient random walks in mixing random environments. One of the advantages of this method over what has been used so far is that it is not restricted to i.i.d. environments.
-
作者：Fernique, X
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Let G be a Gaussian vector taking its values in a separable Frechet space E. We denote by gamma its law and by (H, parallel to(.)parallel to) its reproducing Hilbert space. Moreover, let X be an E-valued random vector of law mu. In the first section, we prove that if mu is absolutely continuous relative to gamma, then there exist necessarily a Gaussian vector G' of law gamma and an H-valued random vector Z such that G' + Z has the law mu of X. This fact is a direct consequence of concentration...
