Existence and regularity of law density of a pair (diffusion, first component running maximum)

Laure Coutin and Monique Pontier

Statistics & Probability Letters, 2019, vol. 153, issue C, 130-138

Abstract: Let X be a continuous d-dimensional diffusion process and M the running supremum of the first component. We show that, ∀t>0, the law of the (d+1) random vector (Mt,Xt) admits a density with respect to the Lebesgue measure using Malliavin’s calculus. In case d=1 we prove the regularity of this density.

Keywords: Running supremum process; Joint law density; Malliavin calculus; Regularity of the density (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.05.013

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