Publication at Faculty of Mathematics and Physics |
2018
Abstract
A linear-quadratic optimal control problem with an infinite time horizon for a scalar linear stochastic differential equation with additive Rosenblatt noise is formulated and solved. The Rosenblatt process is a non-Gaussian continuous stochastic process which exhibits self-similarity and long-range dependence.
The feedback form of the optimal control and the optimal cost are given explicitly. The main tool used to find the optimal control is an Itô-type formula for a Rosenblatt process with drift.