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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Vydáno v:Modern Stochastics: Theory and Applications Ročník 11; číslo 3; s. 303 - 321
Hlavní autoři: Nakagawa, Takuya, Suzuki, Ryoichi
Médium: Journal Article
Jazyk:angličtina
Vydáno: VTeX 2024
Témata:
density functions
Lévy processes
Malliavin calculus
Running maximum
Stochastic differential equations
ISSN:2351-6046, 2351-6054
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Shrnutí: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