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Applications of a formula for the variance function of a stochastic process

Author

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  • Fan, Ruzong
  • Lange, Kenneth
  • Peña, Edsel

Abstract

This paper uses Itô's formula to obtain a representation of the variance function of a class of stochastic processes having right continuous paths with left limits. The representation allows one to generalize recent results of Ball and Faddy concerning over- and under-dispersion of pure birth processes. An application to a cumulative damage model in reliability illustrates the generalization. For many well-known jump and diffusion processes, the representation yields an ordinary differential equation that can be explicitly solved for the variance function.

Suggested Citation

  • Fan, Ruzong & Lange, Kenneth & Peña, Edsel, 1999. "Applications of a formula for the variance function of a stochastic process," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 123-130, June.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:2:p:123-130
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    Cited by:

    1. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2571-2591, November.

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