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作者：Mézières, S; Roynette, B
作者单位：Universite de Lorraine
摘要：This paper is concerned with the simulation of a a-dimensional stochastic differential equation motivated by some physical phenomena of fluid mechanics. The drift and diffusion coefficients of the equation admitting local singularities, we are led to study a particular term of strong perturbation denoted by Brownian impulse. Our suggestion for the simulation is to replace the singularity by a jump on which our study therefore focuses.
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作者：Fournier, N
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a two-dimensional Kac equation without cutoff, which we relate to a stochastic differential equation. We prove the existence of a solution for this SDE, and we use the Malliavin calculus (or stochastic calculus of variations) to prove that the law of this solution admits a smooth density with respect to the Lebesgue measure on R-2. This density satisfies the Kac equation.
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作者：Kumar, S
作者单位：Stanford University
摘要：One of the successes of the Brownian approximation approach to dynamic control of queueing networks is the design of a control policy for closed networks with two servers by Harrison and Wein. Adopting a Brownian approximation with only heuristic justification, they interpret the optimal control policy for the Brownian model as a static priority rule and conjecture that this priority rule is asymptotically optimal as the closed networks's population becomes large. This paper studies closed que...
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作者：Glazebrook, KD; Wilkinson, DJ
作者单位：Newcastle University - UK
摘要：We utilize and develop elements of the recent achievable region account of Gittins indexation by Bertsimas and Nino-Mora to design index-based policies for discounted multi-armed bandits on parallel machines. The policies analyzed have expected rewards which come within an O(alpha) quantity of optimality, where alpha > 0 is a discount rate. In the main, the policies make an initial once for all allocation of bandits to machines, with each machine then handling its own workload optimally. This ...
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作者：Méléard, S
作者单位：Universite Paris Nanterre
摘要：We consider the Navier-Stokes equation in dimension 2 and more precisely the vortex equation satisfied by the curl of the velocity field. We show the relation between this equation and a nonlinear stochastic differential equation. Next we use this probabilistic interpretation to construct approximating interacting particle systems which satisfy a propagation of chaos property: the laws of the empirical measures tend, as the number of particles tends to infinity, to a deterministic law for whic...
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作者：Rhee, WT
作者单位：University System of Ohio; Ohio State University
摘要：A packing of a collection of rectangles contained in [0, 1](2) is a disjoint subcollection; the wasted space is the measure of the area of the part of [0, 1]2 not covered by the subcollection. A simple packing has the further restriction that each vertical line meets at most one rectangle of the packing. Given a collection of N independent uniformly distributed subrectangles of [0, 1], we proved in a previous work that there exists a number K such that the wasted space W-N in an optimal simple...
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作者：Jaffard, S
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We prove that the Holder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.
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作者：Fleischmann, K; Klenke, A
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：In this paper we investigate the structure of the equilibrium state of three-dimensional catalytic super-Brownian motion where the catalyst is itself a classical super-Brownian motion. We show that the reactant has an infinite local biodiversity or genetic abundance. This contrasts to the finite local biodiversity of the equilibrium of classical super-Brownian motion. Another question we address is that of extinction of the reactant in finite time or in the long-time Limit in dimensions d = 2,...
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作者：Knessl, C
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We consider an M/M/infinity queue with servers ranked as {1, 2, 3,...}. The Poisson arrival stream has rate lambda and each server works at rate mu. A new arrival takes the lowest ranked available server. We let S be the set of occupied servers and ISI is the number of elements of S. We study the distribution of max(S) in the asymptotic limit of rho = lambda/mu --> infinity. Setting P(m) = Pr [max(S) > m] we find that the asymptotic structure of the problem is different according as m = O(1) o...
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作者：Last, G; Schassberger, R
作者单位：Braunschweig University of Technology
摘要：We consider a random surface Phi in R-d tessellating the space into cells and a random vector held u which is smooth on each cell but may jump on Phi. Assuming the pair (Phi, u) stationary we prove a relationship between the stationary probability measure P and the Palm probability measure P-Phi, of P with respect to the random surface measure associated with Phi. This result involves the flow of u induced on the individual cells and generalizes a well-known inversion formula for stationary po...
