Acta Mathematica Vietnamica
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A Local Limit Theorem for Nonlattice Multidimensional Random Walks in Cones
D. C. Pham , M. Peigné , D. T. Sonpp. 1-21
Abstract
We study the asymptotic behavior of a nonlattice random walk in a general cone of $\mathbb {R}^d$. 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.