Generalisation of Hajek s stochastic comparison results to stochastic sums

TL;DR

This paper extends Hajek's stochastic comparison results to multivariate stochastic sum processes, broadening their applicability to various convex data functions with and without drift.

Contribution

It generalizes Hajek's stochastic comparison to multivariate processes and unifies the results for processes with different drift conditions.

Findings

Extended stochastic comparison to multivariate sums.

Unified univariate and multivariate results.

Applicable to processes with and without drift.

Abstract

Hajek's stochastic comparison result is generalised to multivariate stochastic sum processes with univariate convex data functions and for univariate monoton nondecreasing convex data functions for processes with and without drift respectively. The univariate result is recovered.