Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 1: 161 - 172

DOI: https://doi.org/10.1007/s11464-017-0659-7

RESEARCH ARTICLE

Density functions of doubly-perturbed stochastic differential equations with jumps

  • Yulin SONG
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  • Department of Mathematics, Nanjing University, Nanjing 210093, China

Received date: 14 Jul 2017

Accepted date: 15 Aug 2017

Published date: 12 Jan 2018

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We consider a real-valued doubly-perturbed stochastic differential equation driven by a subordinated Brownian motion. By using classic Malliavin calculus, we prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure on ℝ.

Key words： Doubly-perturbed stochastic differential equations (SDEs); absolute continuity; Malliavin calculus; subordinated Brownian motions

Cite this article

Yulin SONG . Density functions of doubly-perturbed stochastic differential equations with jumps[J]. Frontiers of Mathematics in China, 2018 , 13(1) : 161 -172 . DOI: 10.1007/s11464-017-0659-7

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