Parameter Estimation and Optimal Filtering for Fractional Type Stochastic Systems

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Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process (2002, methodology): “Here, applying the Girsanov type formula for fBm’s which is proved in [ 5 ], it is readily seen that the likelihood ratio between the hypothesis \the parameter value is zero" and the alternative \the parameter value is µ" is given by”
Statistical aspects of the fractional stochastic calculus (2006, background): “Our stochastic analytic tools constitute a new possibility, judging by the fact that the case of H < 1=2 is well within the reach of our tools, in contrast with the other above-mentioned methods, as employed in particular in [23] (see however a general Bayesian-type problem discussed in [24]).”
Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion (2008, methodology): “By a Girsanov-type formula (see, for example, Kleptsyna et al. [ 7, Theorem 3 ]), the measure in the space of continuous, RN-valued functions, generated by the process”