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4395 results in Advances in Applied Probability

Page 189 of 220

  • Stability theorems

  • Eugene Lukacs
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 2 / June 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 336-361
    Print publication:
    June 1977

  • A stability theorem determines the extent to which the conclusions of a given theorem are affected if the assumptions of the theorem are not exactly but only approximately satisfied. The meaning of the word ‘approximately’ has to be defined exactly. The stability of decomposition theorems, of characterizations by independence and by regression properties are the primary object of the paper.

  • The supremum distribution of a Lévy process with no negative jumps

  • J. Michael Harrison
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 2 / June 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 417-422
    Print publication:
    June 1977

  • Let be a process with stationary, independent increments and no negative jumps. Let be this same process modified by a reflecting barrier at zero (a storage process). Assuming that – and denote by ψ(s) the exponent function of X. A simple formula is derived for the Laplace transform of as a function of W(0). Using the fact that the distribution of M is the unique stationary distribution of the Markov process W, this yields an elementary proof that the Laplace transform of M is µs/ψ(s). If it follows that These surprisingly simple formulas were originally obtained by Zolotarev using analytical methods.

  • The geometry of random drift II. The symmetry of random genetic drift

  • Peter L. Antonelli, Jared Chapin, G. Mark Lathrop, Kenneth Morgan
  • Journal:
    Advances in Applied Probability / Volume 9 / Issue 2 / June 1977
    Published online by Cambridge University Press:
    01 July 2016, pp. 250-259
    Print publication:
    June 1977

  • It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.

Page 189 of 220