Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)

TL;DR

This paper revises a previous proof related to small noise asymptotics for invariant densities in diffusions, providing a corrected argument from a control theoretic perspective.

Contribution

It offers a corrected proof for a key theorem on invariant densities in diffusions, clarifying the control theoretic approach.

Findings

Corrected proof of Theorem 5 in the original paper

Clarification of the control theoretic framework

Enhanced understanding of small noise asymptotics

Abstract

The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here a corrected proof.