  We introduce a probabilistic version of the classical Perron's method to
construct viscosity solutions to linear parabolic equations associated to
stochastic differential equations. Using this method, we construct easily two
viscosity (sub and super) solutions that squeeze in between the expected
payoff. If a comparison result holds true, then there exists a unique viscosity
solution which is a martingale along the solutions of the stochastic
differential equation. The unique viscosity solution is actually equal to the
expected payoff. This amounts to a verification result (Ito's Lemma) for
non-smooth viscosity solutions of the linear parabolic equation. This is the
first step in a larger program to prove verification for viscosity solutions
and the Dynamic Programming Principle for stochastic control problems and games
