Parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion

Abstract

This paper is concerned with parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion. Firstly, the state estimation equation is given and the parameter estimator is derived. Then, the strong consistency and asymptotic normality of the maximum likelihood estimator are derived by applying the strong law of large numbers for continuous martingales and the central limit theorem for stochastic integrals with respect to Gaussian martingales. Finally, an example is provided to verify the results.

Keywords

• parameter estimation
• partially observed stochastic differential equations
• fractional brownian motion
• strong consistency
• asymptotic normality