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

Leif Döring (), Lukas Gonon (), David J. Prömel () and Oleg Reichmann
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Leif Döring: University of Mannheim
Lukas Gonon: University of St. Gallen
David J. Prömel: University of Oxford
Oleg Reichmann: European Investment Bank

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 173-205

Abstract: 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.

Keywords: Fokker–Planck equation; Forward Kolmogorov equation; Markov process; Martingale problem; Random time-change; Time-dependent operator; 35Q84; 60J75 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00969-y

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