Smooth density and its short time estimate for jump process determined by SDE

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Ishikawa, Yasushi¹  Kunita, Hiroshi²  Tsuchiya, Masaaki³ 

[1] Ehime Univ, Dept Math, Matsuyama, Ehime 7908577, Japan

[2] Kyushu Univ, Fukuoka 8190395, Japan

[3] Kanazawa Univ, Kanazawa, Ishikawa 9201192, Japan

关键词: Jump process;    Malliavin calculus;    Smooth density;    Short time asymptotics;   

DOI  :  10.1016/j.spa.2017.10.016

来源: Elsevier

【 摘 要 】

We study a nondegenerate jump process on Euclidean space determined by SDE. We show the existence of the smooth density p(s, x; t, y) of its transition probability and its short time asymptotics as t - s -> 0. Assumptions required for these facts are relaxed considerably from past works by Picard and Ishikawa- Kunita. We show these facts using Malliavin calculus on Poisson space. Our calculus is simpler and more efficient than previous works. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free