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• Boundary and entropy of space homogeneous Markov chains AI翻译
  作者：Kaimanovich, VA; Woess, W
  作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Graz University of Technology
  摘要：We study the Poisson boundary (equivalent to representation of bounded harmonic functions) of Markov operators on discrete state spaces that are invariant under the action of a transitive group of permutations. This automorphism group is locally compact, but not necessarily discrete or unimodular. The main technical tool is the entropy theory which we develop along the same lines as in the case of random walks on countable groups, while, however, the implementation is different and exploits di...
• An invariance principle for diffusion in turbulence (vol 27, pg 751, 1999) AI翻译
  作者：Fannjiang, AC; Komorowski, T
  作者单位：Maria Curie-Sklodowska University; University of California System; University of California Davis
• Generalized integration and stochastic ODEs AI翻译
  作者：Flandoli, F; Russo, F
  作者单位：University of Pisa; Universite Paris 13
  摘要：Stochastic forward integrals for processes more general than semimartingales are shown to exist, generalized forms of Ito-Wentzell formula and covariation formula are proved, and one-dimensional stochastic equations driven by finite quadratic variation processes and semimartingales are solved. This generalized stochastic calculus is motivated by applications to uniqueness and dependence on parameters for stochastic equations with nonregular drift.
• Level sets of additive Levy processes AI翻译
  作者：Khoshnevisan, D; Xiao, YM
  作者单位：Utah System of Higher Education; University of Utah; Microsoft
  摘要：We provide a probabilistic interpretation of a class of natural capacities on Euclidean space in terms of the level sets of a suitably chosen multiparameter additive Levy process X. We also present several probabilistic applications of the aforementioned potential-theoretic connections. They include areas such as intersections of Levy processes and level sets, as well as Hausdorff dimension computations.
• Eccentric behaviors of the Brownian sheet along lines AI翻译
  作者：Dalang, RC; Mountford, T
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of California System; University of California Los Angeles
  摘要：Distinct excursion intervals of a Brownian motion (that correspond to a fixed level) have no common endpoints. What is the situation for distinct excursion sets of a Brownian sheet? These sets are termed Brownian bubbles in the literature, and this paper examines how bubbles from fixed or random levels come into contact with each other, by examining whether or not the Brownian sheet restricted to a specific type of curve can have a point of increase. At random levels, we show that points of in...
• Right inverses of nonsymmetric Levy processes AI翻译
  作者：Winkel, M
  作者单位：Sorbonne Universite; Universite Paris Cite
  摘要：We analyze the existence and properties of right inverses K for nonsymmetric Levy processes X, extending recent work of Evans 171 in the symmetric setting. First, both X and -X have right inverses if and only if X is recurrent and has a nontrivial Gaussian component, Our main result is then a description of the excursion measure n(Z) of the strong Markov process Z = X - L (reflected process) where L-t = inf{x > 0 : K-x > t}. Specifically, n(Z) is essentially the restriction of n(X) to the excu...
• An information-geometric approach to a theory of pragmatic structuring AI翻译
  作者：Ay, N
  作者单位：Max Planck Society
  摘要：Within the framework of information geometry, die interaction among units of a stochastic system is quantified in terms of the Kullback-Leibler divergence of the underlying joint probability distribution from an appropriate exponential family. In the present paper, the main example for such a family is given by the set of all factorizable random fields. Motivated by this example, the locally farthest points from an arbitrary exponential family epsilon are studied. In the corresponding dynamica...
• Time-reversal in hyperbolic s.p.d.e.'s AI翻译
  作者：Dalang, RC; Walsh, JB
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of British Columbia
  摘要：This paper studies questions of changes of variables in a class of hyperbolic stochastic partial differential equations in two variables driven by white noise. Two types of changes of variables are considered: naive changes of variables which do not involve a change of filtration, which affect the equation much as though it were deterministic, and changes of variables that do involve a change of filtration, such as time-reversals. In particular, if the process in reversed coordinates does sati...
• Lyapunov exponents for small random perturbations of Hamiltonian systems AI翻译
  作者：Baxendale, PH; Goukasian, L
  作者单位：University of Southern California
  摘要：Consider the stochastic nonlinear oscillator equation (x) double over dot = -x - x(3) + epsilon(2)betax + epsilonsigmax(W) over dot(t) with beta < 0 and sigma not equal 0. If 4beta + sigma(2) > 0 then for small enough epsilon > 0 the system (x, (x) over dot ) is positive recurrent in R-2 \ {(0, 0)}. Now let (λ) over bar(epsilon) denote the top Lyapunov exponent for the linearization of this equation along trajectories. The main result asserts that (λ) over bar(epsilon) = epsilon(2/3)(λ) ove...
• A convergence result for critical reversible nearest particle systems AI翻译
  作者：Mountford, T
  作者单位：University of California System; University of California Los Angeles
  摘要：We consider critical reversible nearest particle systems. We assume that the associated renewal measure has large moments as well as some regularity conditions. It is shown that such processes, started from a nontrivial ergodic translation invariant distribution, converge in distribution to the upper invariant measure.