CONVERGENCE IN VARIATION OF THE JOINT LAWS OF MULTIPLE
STABLE STOCHASTIC INTEGRALS
Abstract: In this note, we are interested in the regularity in the sense of total variation of
the joint laws of multiple stable stochastic integrals. Namely, we show that the
convergence
holds true as long as each kernel
converges when
to in the
Lorentz-type space
for .
This result generalizes [4] from the one-dimensional case to the joint law case. It generalizes
also [6] from the Wiener-It setting to the stable setting and [5] in the study of joint law of
multiple stable integrals.
2000 AMS Mathematics Subject Classification: Primary: 60F99, 60G52, 60H05;
Secondary: 60G57.
Key words and phrases: Convergence in variation, multiple stochastic integrals, stable
process, LePage representation, method of superstructure.