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

被引：2

作者：

Coutin, Laure ^{[1
]}

Pontier, Monique ^{[2
]}

机构：

[1] IMT, UMR 5219, Toulouse, France

[2] Univ Paul Sabatier, IMT, F-31062 Toulouse, France

来源：

STATISTICS & PROBABILITY LETTERS | 2019年 / 153卷

关键词：

Running supremum process; Joint law density; Malliavin calculus; Regularity of the density; TIME;

D O I：

10.1016/j.spl.2019.05.013

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let X be a continuous d-dimensional diffusion process and M the running supremum of the first component. We show that, for all 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. (C) 2019 Elsevier B.V. All rights reserved.

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页码：130 / 138

页数：9

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