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作者：Bryc, W; Wesolowski, J
作者单位：University System of Ohio; University of Cincinnati; Warsaw University of Technology
摘要：We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the Meixner polynomials. Special cases of these processes are known to arise from the non-commutative generalizations of the Levy processes.
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作者：Ben Arous, G; Bogachev, LV; Molchanov, SA
作者单位：New York University; University of Leeds; University of North Carolina; University of North Carolina Charlotte
摘要：We study limiting distributions of exponential sums S-N( t) = Sigma(N)(i=1) e(tXi) as t --> infinity, N --> infinity, where (X-i) are i. i. d. random variables. Two cases are considered: (A) ess sup X-i = 0 and ( B) ess sup X-i = infinity. We assume that the function h(x) = - log P{X-i > x} (case B) or h( x) = - logP{X-i > rho < infinity} ( case A) is regularly varying at 8 with index 1 < rho < infinity(case B) or 0 < rho < infinity(case A). The appropriate growth scale of N relative to t is o...
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作者：Ossiander, M
作者单位：Oregon State University
摘要：A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in R-3 with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations of functionals of a Markov process indexed by the nodes of a binary tree. It gives existence and uniqueness of weak solutions for all time under relatively simple conditions on the forcing and initial data. These conditions involve comparison of the forcing and initi...
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作者：Athreya, SR; Swart, JM
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; University of Erlangen Nuremberg
摘要：We study the ergodic behavior of systems of particles performing independent random walks, binary splitting, coalescence and deaths. Such particle systems are dual to systems of linearly interacting Wright-Fisher diffusions, used to model a population with resampling, selection and mutations. We use this duality to prove that the upper invariant measure of the particle system is the only homogeneous nontrivial invariant law and the limit started from any homogeneous nontrivial initial law.
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作者：Blache, F
摘要：The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problems on manifolds.
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作者：Landim, C; Neto, JN
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider reversible, conservative Ginzburg-Landau processes in a random environment, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. We prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L-2 almost surely with respect to the environment.
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作者：Forrester, PJ; Rains, EM
作者单位：University of Melbourne; AT&T
摘要：Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue PDF for a single classical ensemble with unitary symmetry, while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry. We...
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作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let Gamma(n)=(gamma(ij)) be an nxn random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W-n:=max(1less than or equal toi,jless than or equal ton)|gamma(ij)|. We obtain the limiting distribution and a strong limit theorem on W-n. A tool has been developed to prove these results. It says that up to n/(log n)(2) columns of Gamma(n) can be approximated simultaneously by those of some Y-n=(y(ij)) in which y(ij) are independent standard norma...
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作者：Warren, J
作者单位：University of Warwick; University of California System; University of California Berkeley
摘要：A stochastic flow of homeomorphisms of R previously studied by Bass and Burdzy [2] and Hu and Warren [4] is shown to arise in the study of the local times of Brownian motion. This leads to a new proof of the Ray-Knight theorems for the flow via the classical Ray-Knight theorems for Brownian motion.
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作者：Delmotte, T; Deuschel, JD
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Technical University of Berlin
摘要：We consider diffusions on R-d or random walks on Z(d) in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence and Holder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives. In the case of random walks, these estimates are applied to the Ginzburg-Landau del phi interface model.
