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Title: Entropy Dissipation for Degenerate Stochastic Differential Equations via Sub-Riemannian Density Manifold

We studied the dynamical behaviors of degenerate stochastic differential equations (SDEs). We selected an auxiliary Fisher information functional as the Lyapunov functional. Using generalized Fisher information, we conducted the Lyapunov exponential convergence analysis of degenerate SDEs. We derived the convergence rate condition by generalized Gamma calculus. Examples of the generalized Bochner’s formula are provided in the Heisenberg group, displacement group, and Martinet sub-Riemannian structure. We show that the generalized Bochner’s formula follows a generalized second-order calculus of Kullback–Leibler divergence in density space embedded with a sub-Riemannian-type optimal transport metric.

 
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Award ID(s):
2306769 2038080
PAR ID:
10506173
Author(s) / Creator(s):
;
Publisher / Repository:
MDPI
Date Published:
Journal Name:
Entropy
Volume:
25
Issue:
5
ISSN:
1099-4300
Page Range / eLocation ID:
786
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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