REGULARIZATION OF QUASILINEAR HEAT EQUATIONS BY A FRACTIONAL NOISE

Abstract

We show the existence and uniqueness of a solution for a quasilinear parabolic equation in one dimension driven by an additive fractional white noise, assuming that the drift is measurable and satisfies a suitable integrability condition. The proof is based on Girsanov theorem and lower estimates of the density of the solution of the equation without drift.