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作者：Yilmaz, Atilla
作者单位：University of California System; University of California Berkeley
摘要：We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on Z(d). There exist variational formulae for the quenched and averaged rate functions I(q) and I(a), obtained by Rosenbluth and Varadhan, respectively. I(q) and I(a) are not identically equal. However, when d >= 4 and the walk satisfies the so-called (T) condition of Sznitman, they have been previously shown to be equal on an open set A(eq). For every xi is an element of A(eq), we prove th...
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作者：Blachere, Sebastien; den Hollander, Frank; Steif, Jeffrey E.
作者单位：Aix-Marseille Universite; Leiden University; Leiden University - Excl LUMC; Chalmers University of Technology; University of Gothenburg
摘要：In this paper, we consider a random walk and a random color scenery on Z. The increments of the walk and the colors of the scenery are assumed to be i.i.d. and to be independent of each other. We are interested in the random process of colors seen by the walk in the course of time. Bad configurations for this random process are the discontinuity points of the conditional probability distribution for the color seen at time zero given the colors seen at all later times. We focus on the case wher...
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作者：Benaych-Georges, Florent; Levy, Thierry
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for noncommutative random variables. These notions are related to the liberation process introduced by Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated t...
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作者：Applebaum, David
作者单位：University of Sheffield
摘要：We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type measures. We find conditions for such a measure to have a smooth density and give examples. The Hunt semigroup and generator of convolution semigroups of measures are represented as pseudo-differential operators. For sufficiently regular convolution semigrou...
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作者：Benaim, Michel; Tarres, Pierre
作者单位：University of Neuchatel; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We generalize a result from Volkov [Ann. Probab. 29 (2001) 66-91] and prove that, on a large class of locally finite connected graphs of bounded degree (G, similar to)and symmetric reinforcement matrices a = (a(i), (j))(i),(j is an element of G), the vertex-reinforced random walk (VRRW) eventually localizes with positive probability on subsets which consist of a complete d-partite subgraph with possible loops plus its outer boundary. We first show that, in general, any stable equilibrium of a ...
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作者：Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Manchester
摘要：Given a stable Levy process X = (X-t)(0 <= t <= T) of index alpha is an element of (1, 2) with no negative jumps, and letting S-t = sup(0 <= s <= t) X-s denote its running supremum for t is an element of [0, T], we consider the optimal prediction problem V = inf(0 <=tau <= T) E(S-T - X-tau)(p), where the infimum is taken over all stopping times tau of X, and the error parameter p is an element of(1, alpha) is given and fixed. Reducing the optimal prediction problem to a fractional free-boundar...
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作者：Beiglboeck, Mathias; Schachermayer, Walter; Veliyev, Bezirgen
作者单位：University of Vienna
摘要：We give an elementary proof of the celebrated Bichteler-Dellacherie theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S = M + A, where M is a local martingale and A is a finite variation process. In other words, S is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposit...
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作者：Bordenave, Charles; Lelarge, Marc; Salez, Justin
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G(n))(n >= 0) converging locally to a Galton-Watson tree T (GWT), we provide an explicit formula for the asymptotic multiplicity of the eigenvalue 0 in terms of the degree generating function phi(*) of T. In the first part, we show that the adjacency operator associated with T is always self-adjoint; we analyze the associated spectral measure at the root and characterize the distribution o...
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作者：Baxendale, Peter
作者单位：University of Southern California
摘要：This is a brief survey of T. E. Harris's work on recurrent Markov processes and on stochastic flows, and of some more recent work in these fields.
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作者：Liang, Gechun; Lyons, Terry; Qian, Zhongmin
作者单位：University of Oxford; University of Oxford
摘要：We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither Ito's integrals nor martingale representation formulate are needed. This approach provides new tools for the study of BSDE, and is particularly useful for the study of BSDE with partial information. The approach allows us to study the following type of backward stochastic differential equations: dY(t)(j) = -f(...
