White Noise calculus for time changed Brownian motion
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In this work, we investigate the time change process $\Lambda=(\Lambda_t)_{t\geq0}$ in the framework of infinite dimensional analysis and especially within White Noise calculus. We prove that the time changed Brownian motion is a martingale with respect to an associated enlarged filtration as well as its natural one. Also depending on $\Lambda$, it is not in general a process with independant increments. We define the Hida-Malliavin derivative with respect to the time changed Brownian motion. Finally, we obtain the Clark Ocone formula with respect to the time changed Brownian motion $B_{\Lambda}$.