Stochastic differential equations with generalized stochastic volatility and statistical estimators

We study a stochastic differential equation, the diffusion coefficient of which is a function of some adapted stochastic process. The various conditions for the existence and uniqueness of weak and strong solutions are presented. The drift parameter estimation in this model is investigated, and the strong consistency of the least squares and maximum likelihood estimators is proved. As an example, the Ornstein–Uhlenbeck model with stochastic volatility is considered.