Approximation of a multivariate conditional density

TL;DR

This paper provides a precise approximation for the distribution of long runs of a multivariate light-tailed random walk conditioned on the average of a function of its summands, extending previous asymptotic results.

Contribution

It extends prior work to multivariate light-tailed random walks, offering a sharp approximation for conditioned long runs as the number of summands grows.

Findings

Provides a sharp approximation for conditioned long runs

Extends asymptotic distribution results to multivariate cases

Applicable to light-tailed random walks

Abstract

This paper extends the result of Broniatowski and Caron (2013) pertaining to the asymptotic distribution of a random walk conditioned on its final value as the number of summands increase. We consider multivariate light-tailed random walk and present a sharp approximation of long runs conditioned by an average of a function of its summands as their number tends to infinity.