-
作者：Povel, T
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a large deviation principle for the position at large times t of a one-dimensional annealed Brownian motion in a Poissonian potential in the critical spatial scale t(1/3). Here annealed means that averages are taken with respect to both the path and environment measures. In contrast to the d-dimensional case for d greater than or equal to 2 in. the critical scale t(d/(d + 2)) as treated by Sznitman, the rate function which measures the large deviations exhibits three different regime...
-
作者：Ahn, H
作者单位：University of California System; University of California Santa Barbara
摘要：We provide an integral representation for smooth functionals of continuous semimartingales. The representation is related to an infinite-dimensional nonautonomous parabolic equation. Semimartingale integral representations, including a martingale representation, are given in terms of a solution to this equation.
-
作者：Babillot, M; Bougerol, P; Elie, L
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Let (B-n, A(n))(n greater than or equal to 1) be a sequence of i.i.d. random variables with values in R-d x R-*(+). The Markov chain on R-d which satisfies the random equation X-n = A(n)X(n-1) + B-n is studied when E(log A(1)) = 0. No density assumption on the distribution of (B-1, A(1)) is made. The main results are recurrence of the Markov chain X-n, stability properties of the paths, existence and uniqueness of a Radon invariant measure and a limit theorem for the occupation times. The resu...
-
作者：Liggett, TM; Schonmann, RH; Stacey, AM
作者单位：University of California System; University of California Los Angeles
摘要：We consider families of {0, 1}-valued random variables indexed by the vertices of countable graphs with bounded degree. First we show that if these random variables satisfy the property that conditioned on what happens outside of the neighborhood of each given site, the probability of seeing a 1 at this site is at least a value p which is large enough, then this random field dominates a product measure with positive density. Moreover the density of this dominated product measure can be made ar...
-
作者：Shields, PC
作者单位：University System of Ohio; University of Toledo
摘要：It is known that the length L(x(1)(n)) of the longest block appearing at least twice in a randomly chosen sample path of length it drawn from an i.i.d. process is asymptotically almost surely equal to C log n, where the constant C depends on the process. A simple coding argument will be used to show that for a class of processes called the finite energy processes, L(x(1)(n)) is almost surely upper bounded by C log n, where C is a constant. While the coding technique does not yield the exact co...
-
作者：El Karoui, N; Kapoudjian, C; Pardoux, E; Peng, S; Quenez, MC
作者单位：Sorbonne Universite; Aix-Marseille Universite; Ecole Normale Superieure de Lyon (ENS de LYON); Shandong University; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We study reflected solutions of one-dimensional backward stochastic differential equations. The reflection keeps the solution above a given stochastic process. We prove uniqueness and existence both by a fixed point argument and by approximation via penalization. We show that when the coefficient has a special form, then the solution of our problem is the value function of a mixed optimal stopping-optimal stochastic control problem. We finally show that, when put in a Markovian framework, the ...
-
作者：Benaïm, M
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We discuss and disprove a conjecture of Pemantle concerning vertex-reinforced random walks. The setting is a general theory of non-Markovian discrete-time random processes on a finite space E = {1,...,d}, for which the transition probabilities at each step are influenced by the proportion of times each state has been visited. It is shown that, under mild conditions, the asymptotic behavior of the empirical occupation measure of the process is precisely related to the asymptotic behavior of som...
-
作者：Bramson, M; Cox, JT; Greven, A
作者单位：University of Wisconsin System; University of Wisconsin Madison; Syracuse University; University of Erlangen Nuremberg
摘要：We consider two critical spatial branching processes on R-d: critical branching Brownian motion, and the critical Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension dependent. It is known that in low dimensions, d less than or equal to 2, the only invariant measure is delta(0), the unit point mass on the empty state. In high dimensions, d greater than or equal to 3, there is a family {nu(0), theta is an element of [0, infinity)} of ex...
-
作者：Graham, C; Méléard, S
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Sorbonne Universite
摘要：We specify the Markov process corresponding to a generalized mollified Boltzmann equation with general motion between collisions and nonlinear bounded jump (collision) operator, and give the nonlinear martingale problem it solves. We consider various Linear interacting particle systems in order to approximate this nonlinear process. We prove propagation of chaos, in variation norm on path space with a precise rate of convergence, using coupling and interaction graph techniques and a representa...
-
作者：Bolthausen, E; Schmock, U
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let {X-t}(t greater than or equal to 0) be a symmetric, nearest-neighbor random walk on Z(d) with exponential holding times of expectation 1/d, starting at the origin. For a potential V: Z(d) --> [0, infinity) with finite and nonempty support, define transformed path measures by d (P) over cap(T) = exp(T(-1)integral(0)(T)integral(0)(T)V(X-s - X-t)ds/dt)dP/Z(T) for T > 0, where ZT is the normalizing constant. If d = 1 or if the self-attraction is sufficiently strong, then \\X-t\\(infinity) has ...
