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作者：Nourdin, Ivan
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H. In the quadratic (resp. Cubic) case, when H < 1/4 (resp. H < 1/6). we show by means of Malliavin Calculus that the convergence holds in L(2) toward in explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.
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作者：Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let (Omega, F, P) be a probability space and N the class of those F is an element of F satisfying P(F) is an element of {0, 1}. For each G subset of F, define (G) over bar = sigma(G boolean OR N). Necessary and sufficient conditions for (A) over bar boolean AND (B) over bar = (A boolean AND B) over bar, where A, B subset of F are sub-sigma-fields, are given. These conditions are then applied to the (two-component) Gibbs sampler. Suppose X and Y are the coordinate projections on (Omega, F) = (X...
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作者：Hairer, Martin; Mattingly, Jonathan C.
作者单位：University of Warwick; Duke University
摘要：We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for this analysis is neither a weighted supremum norm nor an LP-type norm, but involves the derivative of the observable as well and hence can be seen as a type of 1-Wasserstein distance. This turns Out to be a suitable approach for infinite-dimensional spaces where the usual Harris or Doeblin conditions, which are geared toward tot...
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作者：Picard, Jean
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
摘要：We consider a real-valued path; it is possible to associate a tree to this path. and we explore the relations between the tree. the properties of p-variation of the path. and integration with respect to the path. In particular. the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include sortie stochastic paths such as marting...
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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Pathwise uniqueness holds for the Skorokhod stochastic differential equation in C1+gamma domains in R-d for gamma > 1/2 and d >= 3.
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作者：Roitershtein, Alexander
作者单位：Iowa State University
摘要：We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429-447]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the environment viewed from the position of the walker converges to a limiting distribution if the environment is an ...
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作者：Pellegrini, Clement
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Recent developments in quantum physics make heavy use of so-called quantum trajectories. Mathematically, this theory gives rise to stochastic Schrodinger equations, that is, perturbation of Schrodinger-type equations under the form of stochastic differential equations. But Such equations are in general not of the usual type as considered in the literature. They pose a serious problem in terms of justifying the existence and uniqueness of a Solution, Justifying the physical pertinence of the eq...
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作者：Dolgopyat, Dmitry; Koralov, Leonid
作者单位：University System of Maryland; University of Maryland College Park
摘要：We consider a process oil 72, which consists of fast motion along the stream lines of ail incompressible periodic vector field perturbed by white noise. It gives rise to a process on the graph naturally associated to the structure of the stream lines Of the unperturbed flow. It has been shown by Freidlin and Wentzell [Random Perturbations of Dynamical Systems, 2nd ed. Springer. New York (1998)] and [Mem. Amer Math. Soc. 109 (1994)] that if the stream function of the flow is periodic. then the ...
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作者：Ma, Jin; Zhang, Jianfeng; Zheng, Ziyu
作者单位：University of Southern California
摘要：In this paper, we propose a new notion of Forward-Backward Martingale, Problem (FBMP), and study its relationship with the weak solution to the forward-backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan. but it is structured specifically to fit the nature of an FBSDE. We first prove a general sufficient condition for the existence of the solution to the FBMP. In the Markovian case with uniformly ...
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Let xi be a Dawson-Watanabe superprocess in R-d such that xi(t) is a.s. locally finite for every t >= 0. Then for d >= 2 and fixed t > 0. the singular random measure xi(t) can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the epsilon-neighborhoods of supp xi(t). When d >= 3. the local distributions of xi(t) near a hitting point can be approximated in total variation by those of a stationary and self-similar pseudo-random measure by contrast, the corresponding ...
