Stability of stochastic integrals under change of filtration

Let ([Omega],,P) be a probability space equipped with two filtrations {t} and {t} satisfying the usual conditions. Assume that X is a semimartingale and that h is locally bounded and predictable for each of the two filtrations {t} and {t}. New examples of such processes are given. Utilizing and extending partial results of Zheng (1982), this paper extends the available results on the relationship between the stochastic integral processes [integral operator]ths dXs taken respectively in the sense of {t} and of {t}. In particular, it is shown that these stochastic integrals differ at most by a continuous process with quadratic variation defined and equal to 0. If both stochastic integrals are {t[intersection]t} semimartingales, then it is proved that the stochastic integral [integral operator]ths dX s taken in {t} sense is indistinguishable from that taken in {t} sense.