Existence of density function for the running maximum of SDEs driven by nontruncated pure-jump Lévy processes

The existence of density function of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a nontruncated pure-jump process is verified. This is proved by the existence of density function of the running maximum of the Wiener–Poisson functionals resulting fr...

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Bibliographic Details
Published in:Modern Stochastics: Theory and Applications Vol. 11; no. 3; pp. 303 - 321
Main Authors: Nakagawa, Takuya, Suzuki, Ryoichi
Format: Journal Article
Language:English
Published: VTeX 2024
Subjects:
density functions
Lévy processes
Malliavin calculus
Running maximum
Stochastic differential equations
ISSN:2351-6046, 2351-6054
Online Access:Get full text
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Summary:The existence of density function of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a nontruncated pure-jump process is verified. This is proved by the existence of density function of the running maximum of the Wiener–Poisson functionals resulting from Bismut’s approach to the Malliavin calculus for jump processes.
ISSN:2351-6046
2351-6054
DOI:10.15559/24-VMSTA245