• Corpus ID: 247155191

Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold

@inproceedings{Feng2019EntropyDF,
  title={Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold},
  author={Qi Feng and Wuchen Li},
  year={2019}
}

• Qi Feng, Wuchen Li
• Published 16 October 2019
• Mathematics

We study the dynamical behavior of degenerate stochastic differential equations (SDEs). We select an auxiliary-Fisher information functional as the Lyapunov functional. We conduct the Lyapunov exponential convergence analysis of degenerate SDEs in terms of generalized Fisher information and $L^1$ distances. We derive the convergence rate by the induced generalized Gamma $z$ calculus. Examples of explicit rates are provided, including one-dimensional degenerate SDEs, gradient-drift diffusions in the Heisenberg group, displacement group, and Martinet sub-Riemannian structure. The Lyapunov analysis is constructed from a second-order calculus of Kullback-Leibler divergence in density space with a sub-Riemannian optimal transport type metric.