  A discretization scheme for nonnegative diffusion processes is proposed and
the convergence of the corresponding sequence of approximate processes is
proved using the martingale problem framework. Motivations for this scheme come
typically from finance, especially for path-dependent option pricing. The
scheme is simple: one only needs to find a nonnegative distribution whose mean
and variance satisfy a simple condition to apply it. Then, for virtually any
(path-dependent) payoff, Monte Carlo option prices obtained from this scheme
will converge to the theoretical price. Examples of models and diffusion
processes for which the scheme applies are provided.
