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作者：Kotelenez, Peter
作者单位：University System of Ohio; Case Western Reserve University
摘要：The Navier-Stokes equation for the vorticity of a viscous and incompressible fluid in R-2 is analyzed as a macroscopic equation for an underlying microscopic model of randomly moving vortices. We consider N point vortices whose positions satisfy a stochastic ordinary differential equation on R-2N, where the fluctuation forces are state dependent and driven by Brownian sheets. The state dependence is modeled to yield a short correlation length e between the fluctuation forces of different vorti...
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作者：Embrechts, P.; Rogers, L. C. G.; Yor, M.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bath; Sorbonne Universite
摘要：An explanation of a remarkable identity in law, due to A. Dassios, concerning the alpha-quantile of Brownian motion with drift is given with the help of Bertoin's rearrangement of positive and negative excursions for Brownian motion with drift.
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作者：Athreya, K. B.; Vidyashankar, A. N.
作者单位：Iowa State University
摘要：Let {Z(n) : n >= 0} be a p-type(p >= 2) supercritical branching process with mean matrix M. It is known that for any l in R-P, (l . Z(n)/1 . Z(n) - l . Z(n)M/1 . Z(n)) and (l . Z(n)/1 . Z(n) - l . upsilon((1))/1 . upsilon((1))) converge to 0 with probability 1 on the set of nonextinction, where upsilon((1)) is the left eigenvector of M corresponding to its maximal eigenvalue rho and 1 is the vector with all components equal to one. In this paper we study the large deviation aspects of this con...
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作者：Francos, Joseph M.; Meiri, A. Zvi; Porat, Boaz
作者单位：Ben-Gurion University of the Negev; Technion Israel Institute of Technology
摘要：Imposing a total order on a regular two-dimensional discrete random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic field. The deterministic component is further orthogonally decomposed into a half-plane deterministic field and a countable number of mutually orthogonal evanescent fields. Each of the evanescent fields is generated by the column-to-column innovations of the deterministic field with respect to a...
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作者：Asmussen, Soren; Glynn, Peter; Pitman, Jim
作者单位：Aalborg University; Stanford University; University of California System; University of California Berkeley
摘要：This paper is concerned with various aspects of the simulation of one-dimensional reflected (or regulated) Brownian motion. The main result shows that the discretization error associated with the Euler scheme for simulation of such a process has both a strong and weak order of convergence of precisely 1/2. This contrasts with the faster order 1 achievable for simulations of SDE's without reflecting boundaries. The asymptotic distribution of the discretization error is described using Williams'...
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作者：Graham, Carl; Meleard, Sylvie
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Sorbonne Universite
摘要：We consider a network in which a call holds a given number of uniformly chosen links and releases them simultaneously. We show pathwise propagation of chaos and convergence of the process of empirical fluctuations to a Gaussian Ornstein-Uhlenbeck process. The limiting martingale problem is obtained by closing a hierarchy. The drift term is given by a simple factorization technique related to mean-field interaction, but the Doob Meyer bracket contains special terms coming from the strong intera...
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作者：Dinwoodie, I. H.
作者单位：Tulane University
摘要：A bound is given for a reversible Markov chain on the probability that the occupation measure of a set exceeds the stationary probability of the set by a positive quantity.
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作者：Mahmoud, Hosam M.
作者单位：George Washington University
摘要：By embedding in a suitable continuous-time process, we find a strong law for h(n), the height of a random binary pyramid of order n. We show that h(n)/ln n converges almost surely to a constant limit and we determine that limit.
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作者：El Karoui, Nicole; Karatzas, Ioannis
作者单位：Sorbonne Universite; Columbia University
摘要：We present an approach to the general, non-Markovian dynamic allocation (or multiarmed bandit) problem, formulated in continuous time as a problem of stochastic control for multiparameter processes in the manner of Mandelbaum. This approach is based on a direct, martingale study of auxiliary questions in optimal stopping. Using a methodology similar to that of Whittle and relying on simple time-change arguments, we construct Gittins-index-type strategies, verify their optimality, provide expli...
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作者：Alexander, Kenneth S.
作者单位：University of Southern California
摘要：Functionals L on finite subsets A of R'1 are considered for which the value is the minimum total edge length among a class of graphs with vertex set equal to, or in some cases containing, A. Examples include minimal spanning trees, the traveling salesman problem, minimal matching and Steiner trees. Beardwood, Halton and Hammersley, and later Steele, have shown essentially that for {X1,, X,,} a uniform i.i.d. sample from [0,1](d), EL({X-1, . . . , X-n})/n((d-1)/d) converges to a finite constant...
