Moderate Deviation Principles for Unbounded Additive Functionals of Distribution Dependent SDEs

TL;DR

This paper establishes moderate deviation principles for unbounded additive functionals of distribution dependent stochastic differential equations, covering models with both non-degenerate and degenerate noises, by comparing original and stationary equations.

Contribution

It introduces a novel approach to derive MDPs for unbounded functionals in distribution dependent SDEs, including degenerate noise cases.

Findings

MDP established for various distribution dependent SDEs

Applicable to models with non-degenerate and degenerate noises

Provides a framework for analyzing deviations in complex stochastic systems

Abstract

By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with non-degenerate and degenerate noises.