# Invariant measures for stochastic functional differential equations

## TL;DR

This paper develops new, broad conditions ensuring the existence of invariant measures and convergence rates for stochastic functional differential equations, extending classical results and achieving optimality.

## Contribution

It introduces generalized conditions for invariant measures in stochastic functional differential equations, extending Veretennikov--Khasminskii criteria and demonstrating their optimality.

## Key findings

- Established new sufficient conditions for invariant measures.
- Proved exponential and subexponential convergence to equilibrium.
- Extended classical criteria to functional differential equations.

## Abstract

We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and for exponential or subexponential convergence to the equilibrium. The obtained conditions extend Veretennikov--Khasminskii conditions for SDEs and are optimal in a certain sense.