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4395 results in Advances in Applied Probability

Page 179 of 220

  • Asymptotic properties of time domain gaussian estimators

  • R. Kohn
  • Journal:
    Advances in Applied Probability / Volume 10 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    01 July 2016, pp. 339-359
    Print publication:
    June 1978

  • We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to non-linear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss–Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.

  • On N-person stochastic games by denumerable state space

  • A. Federgruen
  • Journal:
    Advances in Applied Probability / Volume 10 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    01 July 2016, pp. 452-471
    Print publication:
    June 1978

  • This paper considers non-cooperative N-person stochastic games with a countable state space and compact metric action spaces. We concentrate upon the average return per unit time criterion for which the existence of an equilibrium policy is established under a number of recurrency conditions with respect to the transition probability matrices associated with the stationary policies. These results are obtained by establishing the existence of total discounted return equilibrium policies, for each discount factor α ∈ [0, 1) and by showing that under each one of the aforementioned recurrency conditions, average return equilibrium policies appear as limit policies of sequences of discounted return equilibrium policies, with discount factor tending to one.

    Finally, we review and extend the results that are known for the case where both the state space and the action spaces are finite.

Page 179 of 220