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

Arnab Ganguly; Debasish Chatterjee; John Lygeros; Heinz Koeppl

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

Probability 2011-07-26 v1

Authors: Arnab Ganguly , Debasish Chatterjee , John Lygeros , Heinz Koeppl

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.

Keywords

uniform moment bounds multi-dimensional functions discrete-time stochastic processes negative drift iterated function systems biochemical reaction networks

Cite

@article{arxiv.1107.4749,
  title  = {Uniform moment bounds of multi-dimensional functions of discrete-time stochastic processes},
  author = {Arnab Ganguly and Debasish Chatterjee and John Lygeros and Heinz Koeppl},
  journal= {arXiv preprint arXiv:1107.4749},
  year   = {2011}
}

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26 pages

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

Abstract

Keywords

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