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作者：Taylor, Jonathan E.; Adler, Robert J.
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz-Killing curvatures of these sets. Whereas our motivation is primarily probabilistic, with statistical applications in the background, this formula has also an interpretation as a version of the classic kinematic fundamental formula of integral geometry. All of these aspects ...
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作者：Kurt, Noemi
作者单位：University of Zurich
摘要：We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semi-flexible membrane. d = 4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.
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作者：Duquesne, Thomas
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r) = r(4)(log log l/r)(-3) in super-critical dimensions d >= 5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.
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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.
