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Mathematics > Analysis of PDEs

arXiv:2309.05316 (math)
[Submitted on 11 Sep 2023]

Title:Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations

Authors:Anton Arnold, Amit Einav, Tobias Wöhrer
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Abstract:The goal of this work is to find the sharp rate of convergence to equilibrium under the quadratic Fisher information functional for solutions to Fokker-Planck equations governed by a constant drift term and a constant, yet possibly degenerate, diffusion matrix. A key ingredient in our investigation is a recent work of Arnold, Signorello, and Schmeiser, where the $L^2$-propagator norm of such Fokker-Planck equations was shown to be identical to the propagator norm of a finite dimensional ODE which is determined by matrices that are intimately connected to those appearing in the associated Fokker-Planck equations.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35Q84, 35H10, 35K10, 35B40
Cite as: arXiv:2309.05316 [math.AP]
  (or arXiv:2309.05316v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2309.05316

Submission history

From: Tobias Wöhrer [view email]
[v1] Mon, 11 Sep 2023 09:04:12 UTC (13 KB)
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