Itô's formula for pseudo-processes (Q1185129)

By using an approach involving conditional expectations, the class of pseudo-processes is considered. For these processes, an Itô-type change of variable formula is given. Afterwards, sufficient conditions concerning some pseudo-processes are given in order that their stochastic integrals to be quasi-martingales (and the connection with the Fölmer measure associated to a pseudo-process is also made). Finally, quasi- martingales are generated as stochastic integrals with respect to Brownian motion-like processes, in which the densities of some pseudo- processes are integrated. Also, the vectorial quasi-martingales are obtained as solutions of some differential stochastic equations concerning pseudo-processes with vector-valued densities.