  By using a simple observation that the density processes appearing in Ito's
martingale representation theorem are invariant under the change of measures,
we establish a non-linear version of the Cameron-Martin formula for solutions
of a class of systems of quasi-linear parabolic equations with non-linear terms
of quadratic growth. We also construct a local stochastic flow and establish a
Bismut type formula for such system of quasi-linear PDEs. Gradient estimates
are obtained in terms of the probability representation of the solution.
Another interesting aspect indicated in the paper is the connection between the
non-linear Cameron-Martin formula and a class of forward-backward stochastic
differential equations(FBSDEs).
