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2 results

  • Ruin Probability for the Integrated Gaussian Process with Force of Interest

  • Part of
  • Xiaoxia He, Yijun Hu
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 3 / September 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 685-694
    Print publication:
    September 2007
    • Article
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  • In this paper we obtain the exact asymptotics of the ruin probability for the integrated Gaussian process with force of interest. The results obtained are consistent with those obtained for the case in which there is no force of interest.

  • Exact overflow asymptotics for queues with many Gaussian inputs

  • Part of
  • Krzysztof Dębicki, Michel Mandjes
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 3 / September 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 704-720
    Print publication:
    September 2003

  • In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.