Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations

Döring, Leif ; Gonon, Lukas ; Prömel, David J. ; Reichmann, Oleg

URL: https://arxiv.org/abs/1812.08579
Additional URL: https://arxiv.org/pdf/1812.08579.pdf
Document Type: Working paper
Year of publication: 2018
Place of publication: Mannheim [u.a.]
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematical Finance (Prömel 2019-)
School of Business Informatics and Mathematics > Probability Theory (Döring 2017-)
Subject: 510 Mathematics
Abstract: We prove existence and uniqueness of solutions to Fokker-Planck equations associated to 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 neither globally bounded nor 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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