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4395 results in Advances in Applied Probability

Page 193 of 220

  • Discrete time methods for simulating continuous time Markov chains

  • Arie Hordijk, Donald L. Iglehart, Rolf Schassberger
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 4 / December 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 772-788
    Print publication:
    December 1976

  • This paper discusses several problems which arise when the regenerative method is used to analyse simulations of Markov chains. The first problem involves calculating the variance constant which appears in the central limit theorem used to obtain confidence intervals. Knowledge of this constant is very helpful in evaluating simulation methodologies. The second problem is to devise a method for simulating continuous time Markov chains without having to generate exponentially distributed holding times. Several methods are presented and compared. Numerical examples are given to illustrate the computional and statistical efficiency of these methods.

  • On generalising the notion of upcrossings to random fields

  • Robert J. Adler
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 4 / December 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 789-805
    Print publication:
    December 1976

  • The aim of the current paper is twofold. Primarily we wish to extend some of our earlier results on excursions of random fields and introduce a more powerful technique for obtaining the mean value of a certain characteristic of these excursions. Since these results can also be used to tie together the scattered results of previous authors we also include a full review of earlier work in this field.

  • On random processes that are almost strict sense stationary

  • Dag Tj⊘stheim
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 4 / December 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 820-830
    Print publication:
    December 1976

  • An extension of the class of strict sense stationary processes is studied. The extended class represents the strict sense analogy of an extension of wide sense stationary processes considered in an earlier paper [9]. The relations between the various types of processes defined are investigated in the general and in the Gaussian case, and some examples are given. It is shown that associated with a process belonging to the extended class there is a strict sense stationary process. The associated strict sense stationary process is unique iff the original process is ergodic.

  • Branching diffusion processes in population genetics

  • Stanley Sawyer
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 4 / December 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 659-689
    Print publication:
    December 1976

  • A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individuals NA in a (geographical) set A at time t, the covariance of NA and NB for two sets A, B, and the probability I(x, y, u) that two individuals found at locations x, y at time t are of the same genetic type if the population is subject to a selectively neutral mutation rate u. The last also leads to limit laws for the average degree of relationship of individuals in various types of branching random fields. We also find the equations that the mean and bivariate densities satisfy, and explicit formulas when the underlying migration process is Brownian motion.

Page 193 of 220