A local limit theorem for nonlattice multidimensional random walks in cones

Thi da Cam Pham; Marc Peigné; Doan Thai Son

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arXiv · 2603.26228

A local limit theorem for nonlattice multidimensional random walks in cones

Thi da Cam Pham·Marc Peigné·Doan Thai Son

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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.

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Thi da Cam Pham, Marc Peigné, Doan Thai Son. 2026-03-27. A local limit theorem for nonlattice multidimensional random walks in cones. https://arxiv.org/abs/2603.26228

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