Approximating some Volterra type stochastic integrals with applications to parameter estimation

Henrik Hult

Stochastic Processes and their Applications, 2003, vol. 105, issue 1, 1-32

Abstract: We consider Volterra type processes which are Gaussian processes admitting representation as a Volterra type stochastic integral with respect to the standard Brownian motion, for instance the fractional Brownian motion. Gaussian processes can be represented as a limit of a sequence of processes in the associated reproducing kernel Hilbert space and as a special case of this representation, we derive Karhunen-Loéve expansions for Volterra type processes. In particular, a wavelet decomposition for the fractional Brownian motion is obtained. We also consider a Skorohod type stochastic integral with respect to a Volterra type process and using the Karhunen-Loéve expansions we show how it can be approximated. Finally, we apply the results to estimation of drift parameters in stochastic models driven by Volterra type processes using a Girsanov transformation and we prove consistency, the rate of convergence and asymptotic normality of the derived maximum likelihood estimators.

Keywords: Fractional; Brownian; motion; Reproducing; kernel; Hilbert; space; Gaussian; process; Likelihood; function (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (8)

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