English

On the rate of change of Varentropy for Markov diffusion processes

Probability 2023-11-14 v1

Abstract

Relying on the reverse-time space-time harmonic property of the ratio of two solutions of the Fokker-Plank equation, we establish an explicit formula for derivative of the \emph{varentropy} for a Markov diffusion process. The formula involves a nonlinear function of the {\em local free energy} ln(pt(x)/pˉ(x))\ln(p_t(x)/\bar{p}(x)).We then verify that our formula yields the correct result in the simple case of a scalar Gaussian diffusion. In the latter case, varentropy is exponentially decaying to zero.

Keywords

Cite

@article{arxiv.2311.06824,
  title  = {On the rate of change of Varentropy for Markov diffusion processes},
  author = {Michele Pavon},
  journal= {arXiv preprint arXiv:2311.06824},
  year   = {2023}
}