Harnack and Super Poincar\'{e} Inequalities for Generalized Cox-Ingersoll-Ross Model

TL;DR

This paper establishes Harnack and super-Poincaré inequalities for a generalized Cox-Ingersoll-Ross model with degenerate noise, using intrinsic metrics and isoperimetric constants to derive optimal estimates.

Contribution

It introduces a novel approach to handle degenerate noise in the generalized CIR model through intrinsic metrics and coupling methods.

Findings

Derived Harnack inequalities for the generalized CIR model.

Obtained super-Poincaré inequalities with optimal rate estimates.

Addressed degenerate noise using intrinsic metric techniques.

Abstract

In this paper, the Harnack inequalities and super-Poincar\'{e} inequality for generalized CIR model are obtained. Since the noise is degenerate, the intrinsic metric has been introduced to construct the coupling by change of measure. By using isopermetric constant, the optimal estimate of the rate function in the super Poincar\'{e} inequality for the associated Dirichlet form is also obtained.