Existence and regularity of law density of a pair (diffusion, first component running maximum)
Résumé
Let X be a continuous $d$-dimensional diffusion process and M the running supremum of the first component. We show that, for any t>0, the law of the (d+1) random vector (M_t,X_t) admits a density with respect to the Lebesgue measure using Malliavin's calculus. In case $d=1$ we prove the regularity of this density. Abstract Let X be a continuous d-dimensional diusion process and M the running supremum of the rst component. We show that, ∀t > 0, the law of the (d + 1) random vector (M t , X t) admits a density with respect to the Lebesgue measure using Malliavin's calculus. In case d = 1 we prove the regularity of this density.
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