Existence and Uniqueness Results for Time-Inhomogeneous Time-Change Equations and Fokker–Planck Equations

Döring, Leif; Gonon, Lukas; Prömel, David J. and Reichmann, Oleg (2019): Existence and Uniqueness Results for Time-Inhomogeneous Time-Change Equations and Fokker–Planck Equations. In: Journal of Theoretical Probability, Vol. 34, No. 1: pp. 173-205

Abstract

We prove existence and uniqueness of solutions to Fokker–Planck equations associated with Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients. Precise conditions on the time-inhomogeneous coefficients are given. In particular, we do not necessarily require the coefficients to be either globally bounded or bounded away from zero. The approach is based on constructing random time-changes and studying related martingale problems for Markov processes with values in locally compact, complete and separable metric spaces.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0894-9840
• Language: English