We generalize existing limit theory for stochastic integrals driven
by semimartingales and with left-continuous integrands. Joint Skorohod
convergence is replaced with joint finite dimensional convergence plus
an assumption excluding the case when oscillations of the integrand appear
immediately before oscillations of the integrator. Integrands may converge in
a very weak topology. It is also proved that convergence of integrators implies
convergence of stochastic integrals with respect to the same topology.
@article{1041903222,
author = {Jakubowski, Adam},
title = {Convergence in various topologies for stochastic integrals driven
by semimartingales},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 2141-2153},
language = {en},
url = {http://dml.mathdoc.fr/item/1041903222}
}
Jakubowski, Adam. Convergence in various topologies for stochastic integrals driven
by semimartingales. Ann. Probab., Tome 24 (1996) no. 2, pp. 2141-2153. http://gdmltest.u-ga.fr/item/1041903222/