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

✍ Scribed by Ruzong Fan; Kenneth Lange; Edsel Peña

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 104 KB
• Volume: 43
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00198-9

✦ Synopsis

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 di usion processes, the representation yields an ordinary di erential equation that can be explicitly solved for the variance function.