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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.
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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.
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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.
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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 ...
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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...
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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...
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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)...
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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...
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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...
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作者：Kharroubi, Idris; Ma, Jin; Pham, Huyen; Zhang, Jianfeng
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Southern California
摘要：We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a pro...
