-
作者：Ossiander, Mina; Waymire, Ed; Zhang, Qing
作者单位：Oregon State University
摘要：Consider a rooted labelled tree graph tau(n) having a total of n vertices. The width function counts the number of vertices as a function of the distance to the root phi. In this paper we compute large n asymptotic behavior of the width functions for two classes of tree graphs (both random and deterministic) of the following types: (i) Galton-Watson random trees tn conditioned on total progeny and (ii) a class of deterministic self-similar trees which include an expected Galton-Watson tree in ...
-
作者：Flatto, L.
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs
摘要：The M / M / 1 queue is considered in the case in which customers are served in random order. A formula is obtained for the distribution of the waiting time w in the stationary state. The formula is used to show that P(w > l) similar to alpha l (-5/6) exp( -beta l - gamma l(1/3)) as l -> infinity, with the constants alpha, beta, and gamma expressed as functions of the traffic intensity p. The distribution of w for the random order discipline is compared to that of the first in, first out discip...
-
作者：Bean, N. G.; Bright, L.; Latouche, G.; Pearce, C. E. M.; Pollett, P. K.; Taylor, P. G.
作者单位：University of Adelaide; Universite Libre de Bruxelles; University of Queensland
摘要：For evanescent Markov processes with a single transient communicating class, it is often of interest to examine the limiting probabilities that the process resides in the various transient states, conditional on absorption not having taken place. Such distributions are known as quasi-stationary (or limiting-conditional) distributions. In this paper we consider the determination of the quasi-stationary distribution of a general level-independent quasi-birth-and-death process (QBD). This distrib...
-
作者：Jones, Owen Dafydd
作者单位：University of Sheffield
摘要：Using the ergodic theory of nonnegative matrices, conditions are obtained for the L-2 and almost sure convergence of a supercritical multitype branching process with varying environment, normed by its mean. We also give conditions for the extinction probability of the limit to equal that of the process. The theory developed allows for different types to grow at different rates, and an example of this is given, taken from the construction of a spatially inhomogeneous diffusion on the Sierpinski...
-
作者：Adler, Robert; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Cornell University
摘要：We describe the mean rate at which a general absolutely continuous stationary S alpha S process crosses a high level. Only nondegeneracy assumptions are imposed in the case 1 < alpha < 2. The same results hold for 0 < alpha <= 1 under certain conditions, ensuring existence of the required conditional moments and the applicability of the classical integral formula for the expected number of level crossings.
-
作者：Penrose, Mathew D.
作者单位：Durham University
摘要：For n points placed uniformly at random on the unit square, suppose M-n (respectively, M-n(1)) denotes the longest edge-length of the nearest neighbor graph (respectively, the minimal spanning tree) on these points. It is known that the distribution of n pi M-n(2) - log n converges weakly to the double exponential; we give a new proof of this. We show that P[M-n(1) = M-n] -> 1, so that the same weak convergence holds for M-n(1).
-
作者：Bramson, Maury; Neuhauser, Claudia
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a two-dimensional catalytic surface reaction between X and Y-n with Y-n + nX -> nXY, where Y-n is a polymer consisting of n identical atoms, each denoted by Y, and X is a monomer. The reactants X and Y-n are present above the surface in a gaseous phase, and bond to the surface at certain rates. The resulting atoms X and Y on the surface react if they are sufficiently close to each other; the product XY then leaves the surface, A classical example is the oxidation of carbon monoxide...
-
作者：Carmona, Rene A.; Xu, Lin
作者单位：Princeton University
摘要：We consider the diffusive scaling limit for the transport of a passive scalar in a two-dimensional time-dependent incompressible Gaussian velocity field and in the presence of molecular diffusivity. We prove that homogenization holds in this limiting regime and we derive some simple properties of the effective diffusivity tensor.
-
作者：Komorowski, Tomasz; Papanicolaou, George
作者单位：Michigan State University; Stanford University
摘要：We prove that the solution of a system of random ordinary differential equations dX(t)/dt = V(t, X(t) with diffusive scaling, X-epsilon(t) = epsilon X(t/epsilon(2)), converges weakly to a Brownian motion when epsilon down arrow 0. We assume that V(t,X), t is an element of R, X is an element of R-d is a d-dimensional, random, incompressible, stationary Gaussian field which has mean zero and decorrelates in finite time.
-
作者：Schmidli, H.
作者单位：Aarhus University
摘要：In applied probability one is often interested in the asymptotic behavior of a certain quantity. If a regenerative phenomenon can be imbedded, then one has the problem that the event of interest may have occurred but cannot be observed at the renewal points. In this paper an extension to the renewal theorem is proved which shows that the quantity of interest converges. As an illustration an open problem in risk theory is solved.
