# Solvability for Stochastic Control Problems with an Arbitrary Noise Process

Bozenna Pasik-Duncan^{*} and Tyrone Duncan

Some stochastic control problems for continuous time systems are described where optimal controls and optimal costs can be explicitly determined by a direct method. The applicability of this method is demonstrated for the linear quadratic control problem with the system driven by an arbitrary noise process with continuous sample paths, a controlled Brownian motion in a symmetric space and the linear exponential quadratic Gaussian control problem. The problems for linear systems can be modified to allow for considering equations in an infinite dimensional Hilbert space that describe stochastic partial differential equations.

Mathematics Subject Classification: 93E20 58J65

Keywords: optimal stochastic control; stochastic analysis; stochastic partial differential equations

Minisymposion: Stochastic Models, Control and Applications