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Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 32 [1] (1998)Páginas 45-71

Lifting theorems for some classes of two parameters martingales

Myriam Muñoz De Özak
Universidad Nacional de Colombia, Bogotá, COLOMBIA

Abstract. 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.

Palabras claves. Strong, weak, lare and i-martingales. Stochastic processes, lifting of a stochastic process and of a martingale. Stochastic integration. Nonstandard analysis. Brownian motion.

Codigo AMS. 1991 Primary 60G44. Secondary 60G48, 60H05.

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