Renyi information for ergodic diffusion processes

TL;DR

This paper derives explicit formulas for Re9nyi information, Shannon entropy, and Song measure for invariant densities of various one-dimensional ergodic diffusion processes, including several well-known and new models.

Contribution

It provides the first explicit formulas for these information measures across a broad class of ergodic diffusion models, including new skew-t diffusions.

Findings

Explicit formulas for Re9nyi information, Shannon entropy, and Song measure.

Application to hyperbolic, inverse Gaussian, Pearson, exponential, and skew-t diffusions.

Enhanced understanding of information properties of ergodic diffusion processes.

Abstract

In this paper we derive explicit formulas of the R\'enyi information, Shannon entropy and Song measure for the invariant density of one dimensional ergodic diffusion processes. In particular, the diffusion models considered include the hyperbolic, the generalized inverse Gaussian, the Pearson, the exponential familiy and a new class of skew-$t$ diffusions.