Remarks on some linear fractional stochastic equations

Abstract

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings the solution is negative on a non-negligible set.