Invariant Measures of Lévy-driven Stochastic Differential Equations

V. Knopova; Y. Mokanu; R. L. Schilling

Invariant Measures of Lévy-driven Stochastic Differential Equations

Тип публікації :

Препринт

Дата випуску :

24 червня 2026 р.

Автор(и) :

V. Knopova

Y. Mokanu

R. L. Schilling

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/34312

Журнал :

arXiv (Cornell University)

Цитування :

[APA 7] V., K., Y., M., & R., L. S. (2026). Invariant Measures of Lévy-driven Stochastic Differential Equations. arXiv (Cornell University),. https://ir.library.knu.ua/handle/15071834/34312

[ДСТУ] V. K., Y. M., R. L. S. Invariant Measures of Lévy-driven Stochastic Differential Equations. arXiv (Cornell University). 2026. URL: https://ir.library.knu.ua/handle/15071834/34312 (дата звернення: 11.09.2026).

We study the structure and regularity of (infinitesimally) invariant measures of the solutions to stochastic differential equations $dX_t = b(X_t)\,dt + dZ_t$, where $(Z_t)_{t\geq 0}$ is a Lévy process. We show, in particular, that the invariant measure has to satisfy a Volterra-type convolution equation; since we can obtain the kernels explicitly, we are able to apply regularity methods from harmonic analysis. As an application, we get a very short proof -- in any dimension -- of a classic result due to Sato and Yamazato on the form of the invariant measure of a generalized Ornstein--Uhlenbeck process.

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