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作者：Comets, Francis; Popov, Serguei
作者单位：Universite Paris Cite; Universidade de Sao Paulo
摘要：We study branching random walks in random i.i.d. environment in Z(d), d >= 1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of la...
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作者：Dong, Hongjie; Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Time-inhomogeneous controlled diffusion processes in both cylindrical and noncylindrical domains are considered. Bellman's principle and its applications to proving the continuity of value functions are investigated.
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作者：Rassoul-Agha, Firas; Seppalaineni, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + epsilon moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
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作者：Hanen, Albert
作者单位：Universite Paris Nanterre
摘要：We study the covariance (for Gibbs measure) of spins at two sites in the case of a Sherrington-Kirkpatrick model with an external field. When the number of sites of the model grows to infinity, an asymptotic evaluation of the p moments of that covariance allows us to obtain a weak limit theorem, with a generally non-Gaussian limit law.
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作者：Merkl, Franz; Rolles, Silke W. W.
作者单位：University of Munich; Technical University of Munich
摘要：In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given by random weights on the edges. The edge weights decay exponentially in space. The process converges to a stationary process. We provide asymptotic bounds for the range of the random walker up to a given time, showing that it localizes much more than an ordi...
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作者：Talet, Marina
作者单位：Aix-Marseille Universite
摘要：We study Brownian motion in a drifted Brownian potential. Kawazu and Tanaka [J. Math. Soc. Japan 49 (1997) 189-211] exhibited two speed regimes for this process, depending on the drift. They supplemented these laws of large numbers by central limit theorems, which were recently completed by Hu, Shi and Yor [Trans. Amen Math. Soc. 351 (1999) 3915-3934] using stochastic calculus. We studied large deviations [Ann. Probab. 29 (2001) 11731204], showing among other results that the rate function in ...
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作者：Coviello, Rosanna; Russo, Francesco
作者单位：Scuola Normale Superiore di Pisa; Universite Paris 13
摘要：In this paper we discuss existence and uniqueness for a one-dimensional time inhomogeneous stochastic differential equation directed by an F-semi-martingale M and a finite cubic variation process which has the structure Q + R, where Q is a finite quadratic variation process and R is strongly predictable in some technical sense: that condition implies, in particular, that R is weak Dirichlet, and it is fulfilled, for instance, when R is independent of M. The method is based on a transformation ...
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作者：Chalendar, Isabelle; Partington, Jonathan R.
作者单位：Universite Claude Bernard Lyon 1; University of Leeds
摘要：We prove a multivariable approximate Carleman theorem on the determination of complex measures on R-n and R-+(n) by their moments. This is achieved by means of a multivariable Denjoy-Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragmen-Lindelof-type theorem for analytic functions on C-+(n).
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作者：Du Toit, J.; Peskir, G.
作者单位：University of Witwatersrand; University of Manchester
摘要：Given a standard Brownian motion B-mu = (B-t(mu))(0 <= t <= T) with drift mu is an element of R and letting S-t(mu) = max(0 <= s <= t) B-s(mu) for 0 <= t <= T, we consider the optimal prediction problem: V = inf (0 <=tau <= T) E(B-tau(mu) - S-T(mu))(2) where the infimum is taken over all stopping times tau of B-mu. Reducing the optimal prediction problem to a parabolic free-boundary problem we show that the following stopping time is optimal: tau(*) = inf{t(*) <= t <= T vertical bar b(1) (t) <...
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作者：Bergenthum, Jan; Ruedschendorf, Ludger
作者单位：University of Freiburg
摘要：In this paper, we derive comparison results for terminal values of d-dimensional special semimartingales and also for finite-dimensional distributions of multivariate Levy processes. The comparison is with respect to nondecreasing, (increasing) convex, (increasing) directionally convex and (increasing) supermodular functions. We use three different approaches. In the first approach, we give sufficient conditions on the local predictable characteristics that imply ordering of terminal values of...
