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作者：Lytova, A.; Pastur, L.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We consider n x n real symmetric and Hermitian Wigner random matrices n(-1/2)W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n(-1) X*X with independent entries of m x n matrix X. Assuming first that the 4th cumulant (excess) kappa(4) of entries of W and X is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n -> infin...
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作者：Peng, Shige; Yang, Zhe
作者单位：Shandong University
摘要：In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
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作者：Last, Guenter; Thorisson, Hermann
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Iceland
摘要：We introduce and study invariant (weighted) transport-kernels balancing stationary random measures on a locally compact Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu's exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transport-kernels. We then introduce (in a nonstationary setting) the concept of mass-stationarity with ...
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作者：Haas, Benedicte; Pitman, Jim; Winkel, Matthias
作者单位：Universite PSL; Universite Paris-Dauphine; University of California System; University of California Berkeley; University of Oxford
摘要：We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second applica...
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作者：Koenig, Wolfgang; Lacoin, Hubert; Moerters, Peter; Sidorova, Nadia
作者单位：Leipzig University; Universite Paris Cite; University of Bath; University of London; University College London
摘要：The parabolic Anderson problem is the Cauchy problem for the heat equation partial derivative(t)u(t, z) = Delta u(t,z) + xi(z)u(t,z) on (0,infinity) x Z(d) with random potential (xi(z): z is an element of Z(d)). We consider independent and identically distributed potentials, such that the distribution function of (z) converges polynomially at infinity. If u is initially localized in the origin, that is, if u(0, z) = 1(0)(z), we show that, as time goes to infinity, the solution is completely lo...
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of or-fields, which is key for the stability of the nonlinear filter and partially resolv...
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作者：Yor, M.
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France
摘要：Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's h-transform, as well as a summary of Doob's three books. Finally, Doob's 'stochastic triangle' is viewed in the light of the stochastic analysis of the eighties.
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作者：Pinsky, Ross G.
作者单位：Technion Israel Institute of Technology
摘要：Let D not subset of R(d) be an unbounded domain and let B(t) be a Brownian motion in D with normal reflection at the boundary. We study the transcience/recurrence dichotomy, focusing mainly on domains of the form D = {(x,z) is an element of R(l+m) : vertical bar z vertical bar < H(vertical bar x vertical bar)}, where d = l + m and H is a sufficiently regular function. This class of domains includes various horn-shaped domains and generalized slab domains.
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作者：Chatterjee, Shirshendu; Durrett, Rick
作者单位：Cornell University
摘要：If we consider the contact process with infection rate lambda on a random graph on n vertices with power law degree distributions, mean field calculations suggest that the critical value lambda(c) of the infection rate is positive if the power alpha > 3. Physicists seem to regard this as an established fact, since the result has recently been generalized to bipartite graphs by Gomez-Gardefies et al. [Proc. Nad. Acad. Sci. USA 105 (2008) 1399-1404]. Here, we show that the critical value lambda(...
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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：We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from Z(2) by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edge-reinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edge-reinforced random walk hits the boundary of a large box before returning to its starting point.
