-
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.
-
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...
-
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...
-
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...
