Abstract
We pursue the investigations initiated by Donati-Martin [9] and Effros-Popa [10] 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.
Citation
Aurélien Deya. René Schott. "On multiplication in $q$-Wiener chaoses." Electron. Commun. Probab. 23 1 - 16, 2018. https://doi.org/10.1214/17-ECP104
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