On multiplication in q-Wiener chaoses

Aurélien Deya (1) , René Schott (2)

1 IECL - Institut Élie Cartan de Lorraine
2 LORIA - NSS - Department of Networks, Systems and Services

We pursue the investigations initiated by Donati-Martin and Effros-Popa regarding the multiplication issue in the chaoses generated by the $q$-Brownian motion ($q\in (-1,1)$), along two directions: $(i)$ We provide a fully-stochastic approach to the problem and thus make a clear link with the standard Brownian setting; $(ii)$ We elaborate on the situation where the kernels are given by symmetric functions, with application to the study of the $q$-Brownian martingales.

Mots clés: non-commutative stochastic calculus; q-Brownian motion; q-Wiener chaoses

Domaines: Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Aurélien Deya, René Schott. On multiplication in q-Wiener chaoses. Electronic Communications in Probability, 2018, 23, ⟨10.1214/17-ECP104⟩. ⟨hal-01730320v2⟩