- The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion(arXiv)
Author : Yueyang Zheng, Yaozhong Hu
Abstract : In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained
2. Large deviations of slow-fast systems driven by fractional Brownian motion(arXiv)
Author : Siragan Gailus, Ioannis Gasteratos
Abstract : We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index H>1/2 and the fast component is driven by an independent Brownian motion. Working in the framework of Young integration, we use tools from fractional calculus and weak convergence arguments to establish a Large Deviation Principle in the homogenized limit, as the noise intensity and time-scale separation parameters vanish at an appropriate rate. Our approach is based in the study of the limiting behavior of an associated controlled system. We show that, in certain cases, the non-local rate function admits an explicit non-variational form. The latter allows us to draw comparisons to the case H=1/2 which corresponds to the classical Freidlin-Wentzell theory. Moreover, we study the asymptotics of the rate function as H→1/2+ and show that it is discontinuous at H=1/2
