On a stochastic integral equation with respect to a weak martingale

Abstract

1. Introduction. We introduced in [4] the concept of a weak martingale, which is a natural extension of a martingale. The weak martingale property is invariant through all changes of time, but the property is not true with the definition of local martingales. This is the reason for considering weak martingales. We also proved that the theory of stochastic integration of locally bounded previsible processes can be extended to these weak martingales (see