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作者：Chen, Hong
作者单位：University of British Columbia
摘要：Dupuis and Williams proved that a sufficient condition for the positive recurrence and the existence of a unique stationary distribution for a semimartingale reflecting Brownian motion in an orthant (SRBM) is that all solutions of an associated deterministic Skorohod problem are attracted to the origin. In this paper, we derive a sufficient condition under which we can construct an explicit linear Lyapunov function for the Skorohod problem. Thus, this implies a sufficient condition for the sta...
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作者：Kirschenhofer, Peter; Prodinger, Helmut
作者单位：Technische Universitat Wien
摘要：In this tutorial, statistics on the number of people who tie for first place are considered. It is demonstrated that the so-called Rice's method from the calculus of finite differences is a very convenient tool both to rederive known results as well as to gain new ones with ease.
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作者：Lund, Robert B.; Meyn, Sean P.; Tweedie, Richard L.
作者单位：University System of Georgia; University of Georgia; University of Illinois System; University of Illinois Urbana-Champaign; Colorado State University System; Colorado State University Fort Collins
摘要：Let {Phi(t), t >= 0} be a Markov process on the state space [0, infinity) that is stochastically ordered in its initial state. Examples of such processes include server workloads in queues, birth-and-death processes, storage and insurance risk processes and reflected diffusions. We consider the existence of a limiting probability measure pi or and an exponential convergence rate alpha > 0 such that lim (t -> infinity) e(alpha t)sup(Lambda)vertical bar P-x [Phi(t) is an element of A] - pi(A)ver...
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作者：Hajek, Bruce
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：A set of nodes and a set of consumers are given, and to each consumer there corresponds a subset of the nodes. Each consumer has a demand, which is a load to be distributed among the nodes corresponding to the consumer. The load at a node is the sum of the loads placed on the node by all consumers. The load is balanced if no single consumer can shift some load from one node to another to reduce the absolute difference between the total loads at the two nodes. The model provides a setting to st...
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作者：Rhee, Wansoo T.; Talagrand, Michel
作者单位：University System of Ohio; Ohio State University; University System of Ohio; Ohio State University; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：A packing of a collection of subintervals of [0,1] is a pairwise disjoint subcollection of the intervals; its wasted space is the measure of the set of points not covered by the packing. Consider n random intervals, I-1,...,I-n , chosen by selecting endpoints independently from the uniform distribution. We strengthen and simplify the results of Coffman, Poonen and Winkler, and we show that, for some universal constant K and for each t >= 1, with probability greater than or equal to 1 - 1/n(t),...
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作者：Baccelli, Francois; Schmidt, Volker
作者单位：Ulm University
摘要：We give a Taylor series expansion for the mean value of the canonical stationary state variables of open (max, +)-linear stochastic systems with Poisson input process. Probabilistic expressions are derived for coefficients of all orders, under certain integrability conditions. The coefficients in the series expansion are the expectations of polynomials, known in explicit form, of certain random variables defined from the data of the (max, +)linear system. These polynomials are of independent c...
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作者：Katehakis, Michael N.; Rothblum, Uriel G.
作者单位：Rutgers University System; Rutgers University Newark; Rutgers University New Brunswick; Technion Israel Institute of Technology
摘要：We express Gittins indices for multi-armed bandit problems as Laurent expansions around discount factor 1. The coefficients of these expansions are then used to characterize stationary optimal policies when the optimality criteria are sensitive-discount optimality (otherwise known as Blackwell optimality), average-reward optimality and average-overtaking optimality. We also obtain bounds and derive optimality conditions for policies of a type that continue playing the same bandit as long as th...
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作者：Ferrari, P. A.; Kesten, H.; Martinez, S.
作者单位：Universidade de Sao Paulo; Cornell University; Universidad de Chile
摘要：We prove that certain (discrete time) probabilistic automata which can be absorbed in a null state have a normalized quasi-stationary distribution (when restricted to the states other than the null state). We also show that the conditional distribution of these systems, given that they are not absorbed before time n, converges to an honest probability distribution; this limit distribution is concentrated on the configurations with only finitely many active or occupied sites. A simple example t...
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作者：Dassios, Angelos
作者单位：University of London; London School Economics & Political Science
摘要：The purpose of this note is to obtain a representation of the distribution of the alpha-quantile of a process with stationary and independent increments as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for a Brownian motion. The proof is based on already known discrete time results.
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作者：Diaconis, P.; Saloff-Coste, L.
作者单位：Harvard University; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous time. Some aspects of the theory simplify considerably with finite state spaces and we are able to give a self-contained development. Examples of applications include the study of a Metropolis chain f...
