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Convergence in variation of the joint laws of multiple stable stochastic integrals

Breton J. -C

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

21--40

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 [formula] holds true as long as each kernel finconverges when n→+∞to fi in the Lorentz-type space [formula]. This result generalizes [4] from the one-dimensional case to the joint law case. It generalizes also [6] from the Wiener–Itô setting to the stable setting and [5] in the study of joint law of multiple stable integrals.