Andriy Andreev: Towards Simulation and Inference for the fOU2

Fractional Ornstein-Uhlenbeck process of the second kind is a stationary Gaussian process that extends standard class of Ornstein-Uhlenbeck processes. We introduce it as a solution of stochastic differential equation and characterize by covariance function. We show how to simplify the covariance function on order to utilize in simulation studies. After applying Lamperti-type transformation, we will discuss Euler-Maruyama, Milstein approximation methods to simulate fOU2 and contrast them with exact simulations that employ Circular Embedded Method.