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作者：Liorit, G
作者单位：Universite de Poitiers
摘要：A kind of Laplace's method is developped for iterated stochastic integrals where integrators are complex standard Brownian motions. Then it is used to extend properties of Bougerol and Jeulin's path transform in the random case when simple representations of complex semisimple Lie algebras are not supposed to be minuscule.
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作者：Guionnet, A; Maïda, M
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The estimation of various matrix integrals as the size of the matrices goes to infinity is motivated by theoretical physics, geometry and free probability questions. On a rigorous ground, only integrals of one matrix or of several matrices with simple quadratic interaction (called AB interaction) could be evaluated so far (see e.g. [19], [17] or [9]). In this article, we follow an idea widely developed in the physics literature, which is based on character expansion, to study more complex inte...
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作者：Gallardo, L; Yor, M
作者单位：Universite de Tours; Sorbonne Universite; Universite Paris Cite
摘要：In this paper we give a sufficient condition on the semi group densities of an homogeneous Markov process taking values in R-n which ensures that it enjoys the time-inversion property. Our condition covers all previously known examples of Markov processes satisfying this property. As new examples we present a class of Markov processes with jumps, the Dunkl processes and their radial parts.
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作者：Burdzy, K; Mytnik, L
作者单位：University of Washington; University of Washington Seattle; Technion Israel Institute of Technology
摘要：We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the super-Brownian motion with reflecting historical paths. This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits-they obviously hold for the unique limit found in the present paper.
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作者：Cerrai, S
作者单位：University of Florence; Scuola Normale Superiore di Pisa
摘要：We prove uniqueness, ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction-diffusion equations with multiplicative noise, in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable. To this purpose, we show that the L-1-norm of the difference of two solutions starting from any two different initial data converges P-a.s. to zero, as time goes to infinity.
