Resumen de Lifting theorems for some classes of two parameter martingales

Myriam Muñoz de Özak

• By means of nonstandard analysis we establish some lifting theorems for two parameter stochastic processes, for two parameter martingales and for weak, strong and i-martingales. We also prove that the standard part of an internal martingale is a standard larc martingale (a two parameter version of a càdlàg martingale). A basic nonstandard two parameter stochastic integral is introduced. An integral representation of Wong and Zakai proves to be a very useful tool for our purposes.