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

Author

Listed:
  • Leif Döring

    (University of Mannheim)

  • Lukas Gonon

    (University of St. Gallen)

  • David J. Prömel

    (University of Oxford)

  • Oleg Reichmann

    (European Investment Bank)

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.

Suggested Citation

  • Leif Döring & Lukas Gonon & David J. Prömel & Oleg Reichmann, 2021. "Existence and Uniqueness Results for Time-Inhomogeneous Time-Change Equations and Fokker–Planck Equations," Journal of Theoretical Probability, Springer, vol. 34(1), pages 173-205, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00969-y
    DOI: 10.1007/s10959-019-00969-y
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    References listed on IDEAS

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    2. Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 581-588.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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