Modern Stochastics: Theory and Applications

In this paper, a non-Gaussian Ornstein–Uhlenbeck process driven by a Hermite–Ornstein–Uhlenbeck process is introduced, which belongs to the qth Wiener chaos. A systematic procedure to identify the drift parameter θ and the Hurst parameter H is given based on the study of the limit behavior of its quadratic variations. Estimators for these two parameters and their asymptotic properties are studied.

Multidimensional generalized backward stochastic differential equations (GBSDEs) are studied within a general filtration that supports a Brownian motion under weak assumptions on the associated data. The existence and uniqueness of solutions in ${\mathbb{L}^{p}}$ for $p\in (1,2)$ are established. The results apply to generators that are stochastic monotone in the y-variable, stochastic Lipschitz in the z-variable, and satisfy a general stochastic linear growth condition.