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作者：Graf, Siegfried; Luschgy, Harald; Pages, Gilles
作者单位：University of Passau; Universitat Trier; Universite Paris Cite; Sorbonne Universite
摘要：For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L-r (P)-codebooks alpha(n), and any Voronoi partition V-n,V-a with respect to alpha(n) the local probabilities P(V-n,V-a) satisfy P(V-a,V-n) approximate to n(-1) while the local L-r-quantization errors satisfy integral V-n,V-a parallel to x - a parallel to(r) d P (x) approximate to n(-(1+r/d)) as long as the partition sets V-n,V-a intersect a fixed compact set K in the interior of the support ...
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作者：Heuser, Aaron
作者单位：National Institutes of Health (NIH) - USA
摘要：This paper examines the existence of the self-intersection local time for a superprocess over a stochastic flow in dimensions d <= 3, which through constructive methods, results in a Tanaka-like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the log-Laplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments,...
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作者：Roeckner, Michael; Zhu, Rong-Chan; Zhu, Xiang-Chan
作者单位：University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Peking University
摘要：In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur Rend. Lincei (9) Mat. Appl. 21 (2010) 405-414] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Gamma in a Hilbert space H. We prove the existence and uniqueness of a s...
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作者：Faggionato, Alessandra; Martinelli, Fabio; Roberto, Cyril; Toninelli, Cristina
作者单位：Sapienza University Rome; Roma Tre University; Universite Gustave-Eiffel; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Motivated by several models introduced in the physics literature to study the nonequilibrium coarsening dynamics of one-dimensional systems, we consider a large class of hierarchical coalescence processes (HCP). An HCP consists of an infinite sequence of coalescence processes {xi((n))(.)}(n >= 1); each process occurs in a different epoch (indexed by n) and evolves for an infinite time, while the evolution in subsequent epochs are linked in such a way that the initial distribution of xi((n+1)) ...
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13; University of Alabama System; University of Alabama Huntsville; Michigan State University
摘要：We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d ...
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作者：Kemp, Todd; Nourdin, Ivan; Peccati, Giovanni; Speicher, Roland
作者单位：University of California System; University of California San Diego; Universite de Lorraine; University of Luxembourg; Saarland University
摘要：We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2, the fourth moment of the semicircular law. This extends to the free probabilistic, setting some recent results by Nualart and Peccati on characterizations of central limit theorems in a fixed order of Gaussian Wiener chaos. Our proof is combinatorial, analyz...
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作者：Pittel, Boris
作者单位：University System of Ohio; Ohio State University
摘要：For an ergodic Markov chain {X (t)} on N, with a stationary distribution pi, let T-n > 0 denote a hitting time for [n](c), and let X-n = X (T-n). Around 2005 Guy Louchard popularized a conjecture that, for n -> infinity, T-n is almost Geometric(p), p = pi([n](c)), X-n is almost stationarily distributed on [n](c) and that X-n and T-n are almost independent, if p(n) := sup(i) p(i,[n](c)) -> 0 exponentially fast. For the chains with p(n) -> 0, however slowly, and with sup(i,j) parallel to p(i, .)...
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作者：Diehl, Joscha; Friz, Peter
作者单位：Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Lecture Notes in Control and Inform. Sci. 176 (1992) 200-217] provide a non-Markovian extension to certain classes of nonlinear partial differentia] equations; the nonlinearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in time. To this end, we establish continuity of BSDE solutions with respect to rough path metrics in the sense of Lyons [Re...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let B-s be a d-dimensional Brownian motion and omega(dx) be an independent Poisson field on R-d. The almost sure asymptotics for the logarithmic moment generating function logE(0) exp{+/-theta integral(t)(0)(V) over bar (B-s)ds} (t -> infinity) are investigated in connection with the renormalized Poisson potential of the form (V) over bar (x) = integral(Rd) 1/vertical bar y - x vertical bar(p)[omega(dy) - dy], x is an element of R-d. The investigation is motivated by some practical problems ar...
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作者：Pitman, Jim; Bravo, Geronimo Uribe
作者单位：University of California System; University of California Berkeley
摘要：We offer a unified approach to the theory of convex minorants of Levy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a Levy process on both finite and infinite time intervals, and of a Poisson point process of excursions above the convex minorant up to an independent exponential time. The Poisson Dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a Levy process with cont...
