The fundamental solution of the master equation for a jump‐diffusion Ornstein–Uhlenbeck process

Olga S. Rozanova and Nikolai A. Krutov

Mathematische Nachrichten, 2024, vol. 297, issue 8, 3052-3063

Abstract: An integro‐differential equation for the probability density of the generalized stochastic Ornstein–Uhlenbeck process with jump diffusion is considered for a special case of the Laplacian distribution of jumps. It is shown that for a certain ratio between the intensity of jumps and the speed of reversion, the fundamental solution can be found explicitly, as a finite sum. Alternatively, the fundamental solution can be represented as converging power series. The properties of this solution are investigated. The fundamental solution makes it possible to obtain explicit formulas for the density at each instant of time, which is important, for example, for testing numerical methods.

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202300200

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:8:p:3052-3063

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().