-
作者：Hu, Yaozhong; Nualart, David; Song, Jian
作者单位：University of Kansas
摘要：In this paper we introduce the notion of fractional martingale as the fractional derivative of order a of a continuous local martingale, where alpha is an element of (-1/2, 1/2) and we show that it has a nonzero finite variation of order 2/1+2 alpha, under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Levy's characterization theorem for the fractional Brownian motion.
-
作者：Morris, Ben
作者单位：University of California System; University of California Davis
摘要：We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then We use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling model in 1973: Suppose the number of cards n is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue t...
-
作者：Bloemker, Dirk; Flandoli, Franco; Romito, Marco
作者单位：University of Augsburg; University of Pisa; University of Florence
摘要：The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martin-gale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.
-
作者：Peterson, Jonathon; Zeitouni, Ofer
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider it nearest-neighbor, one dimensional random walk (X-n)(n >= 0) in a random i.i.d. environment. in the regime where the walk is transient but with zero speed, so that X-n is of order n(s) for some s < 1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences {n(k)} and {x(k)} depending on the environment only, such that Xn(k) - x(k) = 0(logn(k))(2) (a localized regime). On the other hand, there exist sequences {t...
-
作者：Rasonyi, Miklos; Schachermayer, Walter; Warnung, Richard
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control; University of Vienna
摘要：In this article we consider a Brownian motion with drift of the form dS(t) = mu(t)dt + dB(t) for t >= 0, with a specific nontrivial (mu(t))(t) >= 0, predictable with respect to F-B, the natural filtration of the Brownian motion B = (B-t)(t >= 0). We construct a process H = (H-t)(t >= 0), also predictable with respect to F-B such that ((H center dot S)(t))(t >= 0) is a Brownian motion in its own filtration. Furthermore, for any delta > 0, we refine this construction such that the drift (mu(t))(...
-
作者：Cattiaux, Patrick; Collet, Pierre; Lambert, Amaury; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Sorbonne Universite; Universite Paris Cite; Universidad de Chile; Universidad de Chile
摘要：In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to -infinity at the origin, and the diffusion to have an entrance boundary at +infinity. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth-death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with pr...
-
作者：Barbu, Viorel; Da Prat, Giuseppe; Tubaro, Luciano
作者单位：Alexandru Ioan Cuza University; Scuola Normale Superiore di Pisa; University of Trento
摘要：We consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Sigma in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Sigma.
-
作者：Doob, J. L.
-
作者：Bressaud, Xavier; Fournier, Nicolas
作者单位：Aix-Marseille Universite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We consider an interacting particle system (eta(t))t >= 0 with values in {0, 1}(Z), in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to its size. We show that such a process admits a unique invariant distribution, which is exponentially mixing and can be perfectly simulated. We also prove that for any initial condition, the avalanche process tends to equilibrium exponentially fast, as time increases to infini...
-
作者：Lowther, George
摘要：In this paper, we took at the properties of limits of a sequence of real valued inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions, then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that we refer to as the almost-continuous diffusions. These processes are strong Markov and satisfy an al...
