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作者：Sellke, Thomas M.
作者单位：Purdue University System; Purdue University
摘要：Suppose a box contains m balls, numbered from 1 to m. A random number of balls are drawn from the box, their numbers are noted and the balls are then returned to the box. This is done repeatedly, with the sample sizes being iid. Let X be the number of samples needed to see all the balls. This paper uses Markov-chain coupling to derive a simple but typically very accurate approximation for EX in terms of the sample size distribution. The approximation formula generalizes the formula found by Po...
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作者：Coffman, E. G., Jr.; Puhalskii, A. A.; Reiman, M. I.
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs; Russian Academy of Sciences
摘要：In polling systems, M >= 2 queues are visited by a single server in cyclic order. These systems model such diverse applications as token-ring communication networks and cyclic production systems. We study polling systems with exhaustive service and zero switchover (walk) times. Under standard heavy-traffic assumptions and scalings, the total unfinished work converges to a one-dimensional reflected Brownian motion, whereas the workloads of individual queues change at a rate that becomes infinit...
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作者：Wormald, Nicholas C.
作者单位：University of Melbourne
摘要：General criteria are given to ensure that in a family of discrete random processes, given parameters exhibit convergence to the solution of a system of differential equations. As one application we consider random graph processes in which the maximum degree is bounded and show that the numbers of vertices of given degree exhibit this convergence as the total number of vertices tends to infinity. Two other applications are to random processes which generate independent sets of vertices in rando...
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作者：Akahori, Jiro
作者单位：University of Tokyo
摘要：In this paper we present an explicit form of the distribution function of the occupation time of a Brownian motion with a constant drift (if there is no drift, this is the well-known arc-sine law). We also define the alpha-percentile of the stock price and give an explicit form of the distribution function of this random variable. Using this explicit distribution, we calculate the price of a new type of path-dependent option, called the alpha-percentile option. This option was first introduced...
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作者：Glasserman, Paul; Kou, Shing-Gang
作者单位：Columbia University; Columbia University
摘要：We consider limits of first passage times to indexed families of nested sets in regenerative processes. The sets are exponentially rare, in the sense that the probability that the process reaches an indexed set in a cycle vanishes exponentially fast in the indexing parameter. Under appropriate formulations of this hypothesis, we prove strong laws, iterated logarithm laws and limits in distribution, both for the index of the rarest set reached in a cycle and for the time to reach a set. An inte...
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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'...
