On stochastic calculus with respect to q-Brownian motion
arXiv:1612.05757 · doi:10.1016/j.jfa.2017.08.019
Abstract
Following the approach and the terminology introduced in [A. Deya and R. Schott, On the rough paths approach to non-commutative stochastic calculus, J. Funct. Anal., 2013], we construct a product L{é}vy area above the -Brownian motion (for ) and use this object to study differential equations driven by the process.We also provide a detailled comparison between the resulting "rough" integral and the stochastic "It{ô}" integral exhibited by Donati-Martin in [C. Donati-Martin, Stochastic integration with respect to Brownian motion, Probab. Theory Related Fields, 2003].