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Volume 47 - March 2010

Contents

Page 5 of 5

Research Article

  • A Simple Model for Random Oscillations

  • Part of:
  • F. Papangelou
  • Published online by Cambridge University Press:
    14 July 2016, pp. 1164-1173
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  • A simple model for a randomly oscillating variable is suggested, which is a variant of the two-state random velocity model. As in the latter model, the variable keeps rising or falling with constant velocity for some time before randomly reversing its direction. In contrast however, its propensity to reverse depends on its current value and it is for this desirable feature that the model is proposed here. This feature has two implications: (a) neither the changing variable nor its velocity is Markovian, although the joint process is, and (b) the linear differential equations arising in the case of our model do not have constant coefficients. The results given in this paper are meant to illustrate the straightforward nature of some of the calculations involved and to highlight the relationship with one-dimensional diffusions.

Back Matter

  • JPR volume 47 issue 1 Cover and Back matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. b1-b3
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Research Article

  • A note on converging geometric-type processes

  • Part of:
  • Maxim Finkelstein
  • Published online by Cambridge University Press:
    14 July 2016, pp. 601-607
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  • The process of deterioration of repairable systems with each repair is modeled using converging geometric-type processes. It is proved that the expectation of the number of repairs in each interval of time is infinite. A new regularization procedure is suggested and the corresponding optimization problem is discussed.

Back Matter

  • JPR volume 47 issue 3 Cover and Back matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. b1-b3
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Research Article

  • Probabilistic Analysis of the Efficacy of Periodic Testing of Employees

  • Part of:
  • Simeon M. Berman
  • Published online by Cambridge University Press:
    14 July 2016, pp. 1174-1190
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  • Some major companies have the policy of annually giving numerical scores to their employees according to their performance, firing those whose performance scores are below a given percentile of the scores of all employees, and then recruiting new employees to replace those who were fired. We introduce a probabilistic model to describe how this practice affects the quality of employee performance as measured over time by the annual scores. Let n be the number of years that the policy has been in effect, and let Fn(x) be the distribution function of the evaluation scores in year n. We show, under certain technical assumptions, that the sequence (Fn(x)) satisfies a particular nonlinear difference equation, and furnish estimates of the solution of the equation and expressions for the quantiles of Fn. The mathematical tools that are used include convex functions, difference equations, and extreme value theory for independent and identically distributed random variables.

Correction

  • Correction

  • Published online by Cambridge University Press:
    14 July 2016, pp. 608-609
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Research Article

  • On Tails of Perpetuities

  • Part of:
  • Paweł Hitczenko
  • Published online by Cambridge University Press:
    14 July 2016, pp. 1191-1194
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  • We establish an upper bound on the tails of a random variable that arises as a solution of a stochastic difference equation. In the nonnegative case our bound is similar to a lower bound obtained in Goldie and Grübel (1996).

Front matter

  • JPR volume 47 issue 2 Cover and Front matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. f1-f4
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Research Article

  • A Central Limit Theorem for Reversible Processes with Nonlinear Growth of Variance

  • Part of:
  • Ou Zhao, Michael Woodroofe, Dalibor Volný
  • Published online by Cambridge University Press:
    14 July 2016, pp. 1195-1202
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  • Kipnis and Varadhan (1986) showed that, for an additive functional, Sn say, of a reversible Markov chain, the condition E[Sn2] / n → κ ∈ (0, ∞) implies the convergence of the conditional distribution of Sn / √E[Sn2], given the starting point, to the standard normal distribution. We revisit this question under the weaker condition, E[Sn2] = nl(n), where l is a slowly varying function. It is shown by example that the conditional distributions of Sn / √E[Sn2] need not converge to the standard normal distribution in this case; and sufficient conditions for convergence to a (possibly nonstandard) normal distribution are developed.

Back matter

  • JPR volume 47 issue 2 Cover and Back matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. b1-b3
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Letter

  • On Perturbed Random Walks

  • Zbigniew Palmowski, Bert Zwart
  • Published online by Cambridge University Press:
    14 July 2016, pp. 1203-1204
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Other

  • Journal of Applied Probability Volume 47 (2010): Index

  • Published online by Cambridge University Press:
    14 July 2016, pp. 1205-1208
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Front Matter

  • JPR volume 47 issue 4 Cover and Front matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. f1-f2
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Back Matter

  • JPR volume 47 issue 4 Cover and Back matter

  • Published online by Cambridge University Press:
    14 July 2016, pp. b1-b8
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Page 5 of 5