-
作者：Mishura, Yuliya; Valkeila, Esko
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Aalto University
摘要：Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Omega, F, P). The classical characterization due to P. Levy says that X is a Brownian motion if and only if X and X-t(2) - t, t >= 0, are martingales with respect to the intrinsic filtration F-X. We extend this result to fractional Brownian motion.
-
作者：Ignatiouk-Robert, Irina; Loree, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite
摘要：A complete representation of the Martin boundary of killed random walks on the quadrant N* x N* is obtained. It is proved that the corresponding full Martin compactification of the quadrant N* x N* is homeomorphic to the closure of the set {w = z/(1 +vertical bar z vertical bar) : Z is an element of N* x N*} in R(2). The method is based on a ratio limit theorem for local processes and large deviation techniques.
-
作者：Castell, Fabienne
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：Let (X(t), t >= 0) be a continuous time simple random walk on Z(d) (d >= 3), and let I(T)(x) be the time spent by (X(t), t >= 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I(T) = Sigma(x is an element of Zd) I(T)(x)(q) in the critical case q = d/d-2. When q is integer, we obtain similar results for the intersection local times of q independent simple random walks.
-
作者：Robert, Raoul; Vargas, Vincent
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this article, we extend the theory of multiplicative chaos for positive definite functions in R-d of the form f(x) = lambda(2) In+ R/vertical bar x vertical bar + g(r), where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in [Am. Sci. Math. Quebec 9 (1985) 105-150]. As a main application, we provide a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent flow.
-
作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：Consider the mutually catalytic branching process with finite branching rate gamma We show that as gamma -> infinity, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give descriptions of this process in terms of its semigroup in terms of the infinitesimal generator and as the solution of a martingale problem We also give a strong construction in terms of a planar Brownian motion from which we infer a path property of the process This ...
-
作者：Kang, Weining; Ramanan, Kavita
作者单位：Carnegie Mellon University
摘要：For a class of stochastic differential equations with reflection for which a certain LP continuity condition holds with p > 1, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum of a local martingale and a continuous, adapted process of zero p-variation. When p = 2, this implies that the reflected diffusion is a Dirichlet process. Two examples are provided to motivate such a characterization. The first example is a class of multidimensional reflec...
-
作者：Lowther, George
摘要：We consider decompositions of processes of the form Y = f (t, X(t)) where X is a semimartingale. The function f is not required to be differentiable, so Ito's lemma does not apply. In the case where f (t, x) is independent of t, it is shown that requiring f to be locally Lipschitz continuous in x is enough for an Ito-style decomposition to exist. In particular, Y will be a Dirichlet process. We also look at the case where f (t, x) can depend on t, possibly discontinuously. It is shown, under s...
-
作者：Bressaud, Xavier; Fournier, Nicolas
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We consider the so-called one-dimensional forest fire process. At each site of Z, a tree appears at rate 1. At each site of Z, a fire starts at rate lambda > 0, immediately destroying the whole corresponding connected component of trees. We show that when lambda is made to tend to 0 with an appropriate normalization, the forest tire process tends to a uniquely defined process, the dynamics of which we precisely describe. The normalization consists of accelerating time by a factor log(1/lambda)...
-
作者：Burdzy, Krzysztof; Swanson, Jason
作者单位：University of Washington; University of Washington Seattle; State University System of Florida; University of Central Florida
摘要：We consider the solution u(x, t) to a stochastic heat equation. For fixed x, the process F(t) = u(x, t) has a nontrivial quartic variation. It follows that F is not a semimartingale, so a stochastic integral with respect to F cannot be defined in the classical Ito sense. We show that for sufficiently differentiable functions g(x, t), a stochastic integral integral g(F(t), t)d F(t) exists as a limit of discrete, midpoint-style Riemann sums, where the limit is taken in distribution in the Skorok...
-
作者：Goldstein, Larry
作者单位：University of Southern California
摘要：Let X-1, X-n be independent with zero means, finite variances sigma(2)(1), sigma(2)(n) and finite absolute third moments Let F-n be the distribution function of (X-1 + + X-n)/sigma where sigma(2) = Sigma(n)(t=1) sigma(2)(t), and Phi that of the standard normal The L-1-distance between F-n and Phi then satisfies parallel to F-n-Phi parallel to(1) <= 1/sigma(3) (n)Sigma E-t=1 vertical bar X-t vertical bar(3) In particular, when X-1. X-n are identically distributed with variance sigma(2). we have...
