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

Ruzong Fan, Kenneth Lange and Edsel Peña

Statistics & Probability Letters, 1999, vol. 43, issue 2, 123-130

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.

Keywords: Compensator; Cumulative; damage; model; Diffusion; process; Ito's; formula; Martingale; Over-; and; under-dispersion; Point; process (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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