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4395 results in Advances in Applied Probability

Page 197 of 220

  • Vector linear time series models

  • W. Dunsmuir, E. J. Hannan
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 2 / June 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 339-364
    Print publication:
    June 1976

  • This paper presents proofs of the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series. The estimators are derived from a Gaussian likelihood (although Gaussianity is not assumed) and certain spectral approximations to this. An important example of finite-parameter models for multiple time series is the class of autoregressive moving-average (ARMA) models and a general treatment is given for this case. This includes a discussion of the problems associated with identification in such models.

  • Bang-bang controls of point processes

  • P. Brémaud
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 2 / June 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 385-394
    Print publication:
    June 1976

  • In this paper, we consider the problem of controlling the intensity of a point process in order to maximize the probability that the number of points in a fixed interval equals a given integer, under the constraint that the intensity belong to some closed interval of R+.

    The problem is stated as a problem of optimization on the set of probabilities over the basic measurable space of point processes, and shown to be equivalent to a problem of deterministic control. Structural results concerning the set of optimal solutions are given. The existence of the latter is proven; the control is shown to be bang-bang and a complete solution can be obtained by application of Pontryagin's Maximum Principle.

  • Queueing output processes

  • D. J. Daley
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 2 / June 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 395-415
    Print publication:
    June 1976

  • The paper reviews various aspects, mostly mathematical, concerning the output or departure process of a general queueing system G/G/s/N with general arrival process, mutually independent service times, s servers (1 ≦ s ≦ ∞), and waiting room of size N (0 ≦ N ≦ ∞), subject to the assumption of being in a stable stationary condition. Known explicit results for the distribution of the stationary inter-departure intervals {Dn} for both infinite and finite-server systems are given, with some discussion on the use of reversibility in Markovian systems. Some detailed results for certain modified single-server M/G/1 systems are also available. Most of the known second-order properties of {Dn} depend on knowing that the system has either Poisson arrivals or exponential service times. The related stationary point process for which {Dn} is the stationary sequence of the corresponding Palm–Khinchin distribution is introduced and some of its second-order properties described. The final topic discussed concerns identifiability, and questions of characterizations of queueing systems in terms of the output process being a renewal process, or uncorrelated, or infinitely divisible.

Page 197 of 220