We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we...

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H1/2$$</EquationSource> </InlineEquation>. Rates of convergence for the approximation task are provided,...</equationsource></inlineequation>

It is commonly accepted that certain financial data exhibit long-range dependence. We consider a continuous-time stochastic volatility model in which the stock price is Geometric Brownian Motion with volatility described by a fractional Ornstein--Uhlenbeck process. We also study two...