Abstract
Homogeneous additive processes on a finite or semi-infinite interval have been studied in many forms. Wald's identity for the first passage process on the finite interval (see for example Miller, 1961), the waiting time process of Lindley (1952), and a variety of problems in the theory of queues, dams, and inventories come to mind. These processes have been treated by and large by methods in the complex plane. Lindley's discrete parameter process on the continuum, for example, described by
where the ξn are independent identically distributed random variables, has been discussed by Wiener-Hopf methods in recent years by Lindley (1952), Smith (1953), Kemperman (1961), Keilson (1961), and many others. A review of earlier studies is given by Kemperman.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference21 articles.
1. A Generalization of Wald's Identity with Applications to Random Walks
2. Local Limit Theorems for Large Deviations
3. The Passage Problem for a Stationary Markov Chain
4. Recurrent random walk and logarithmic potential;Spitzer;Fourth Berkeley Symposium on Statistics and Probability,1961
5. On the asymptotic behaviour of queues;Keilson;J. R. Statist. Soc.,1963 b
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3. The bilateral Laguerre transform;Applied Mathematics and Computation;1981-03
4. Compensation measures in the theory of Markov chains;Stochastic Processes and their Applications;1974-01
5. Asymptotic correlation in a queue;Journal of Applied Probability;1969-12