# Limit Theorems for Additive Functionals of Path-Dependent SDEs

## TL;DR

This paper establishes fundamental limit theorems such as the law of large numbers, central limit theorem, and law of iterated logarithm for additive functionals of path-dependent stochastic differential equations, using advanced probabilistic techniques.

## Contribution

It introduces new limit theorems for path-dependent SDEs by leveraging uniform mixing Markov processes and martingale difference sequences.

## Key findings

- Proved strong law of large numbers for path-dependent SDEs.
- Established central limit theorem in the path-dependent setting.
- Derived law of iterated logarithm for additive functionals.

## Abstract

By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations.