A local limit theorem for nonlattice multidimensional random walks in cones

TL;DR

This paper establishes local limit theorems for nonlattice multidimensional random walks confined to cones, using strong approximation techniques and classical theorems.

Contribution

It extends local limit theorems to nonlattice random walks in cones by combining strong approximation with integral and classical theorems.

Findings

Proves local limit theorems for nonlattice random walks in cones.

Uses strong approximation of random walks by Brownian motion.

Combines integral theorems with classical results for unrestricted walks.

Abstract

We study the asymptotic behavior of a nonlattice random walk in a general cone of $R^d$ . Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove local limit theorems, combining integral theorems for random walks in cones with classical theorems for unrestricted random walks.