Approximating some Volterra type stochastic integrals with applications to parameter estimation
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.
Year of publication: |
2003
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Authors: | Hult, Henrik |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 105.2003, 1, p. 1-32
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Publisher: |
Elsevier |
Keywords: | Fractional Brownian motion Reproducing kernel Hilbert space Gaussian process Likelihood function |
Saved in:
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