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

Arnab Ganguly; Debasish Chatterjee; John Lygeros; Heinz Koeppl

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arXiv · 1107.4749

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

Arnab Ganguly·Debasish Chatterjee·John Lygeros·Heinz Koeppl

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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.

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Arnab Ganguly, Debasish Chatterjee, John Lygeros, Heinz Koeppl. 2011-07-24. Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes. https://arxiv.org/abs/1107.4749

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