Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes

TL;DR

This paper provides conditions ensuring uniform moment bounds for vector-valued functions of discrete-time stochastic processes, with applications to systems like biochemical networks and iterated function systems.

Contribution

It introduces new criteria combining negative drift and jump bounds to establish uniform moment bounds for multi-dimensional stochastic processes.

Findings

Established uniform r-th moment bounds under specified conditions.

Applied results to biochemical reaction networks.

Extended to iterated function systems.

Abstract

We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions include an appropriate negative drift together with a uniform $L_p$ bound on the jumps of the process for $p > r + 1$. Applications of the result are given in connection to iterated function systems and biochemical reaction networks.