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We study a stochastic control system involving both a standard and afractional Brownian motion with Hurst parameter less than 1/2. We apply ananticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on boththe fractional Brownian motion and the standard Brownian motion. We derive amaximum principle and the associated stochastic variational inequality, whichboth are generalizations of the classical case.

Peng's Maximum Principle for a Stochastic Control Problem Driven by a Fractional and a Standard Brownian Motion