• Corpus ID: 117170395

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

@article{Ganguly2011UniformMB,
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: Probability},
year={2011}
}
• Published 24 July 2011
• Mathematics
• arXiv: Probability
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.

## References

SHOWING 1-10 OF 31 REFERENCES

• Mathematics
Journal of Applied Probability
• 2001
We consider Markov chains in the context of iterated random functions and show the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift
In this book invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes are discussed. These Feller processes appear in the study of iterated
• Mathematics
• 2009
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target
• Mathematics
• 2004
We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This
• Mathematics
• 1988
On considere un processus de Markov en temps discret sur un espace metrique localement compact obtenu par iteration aleatoire des cartes de Lipschitz w 1 , w 2 , ..., w n
• Mathematics
SIAM Rev.
• 1999
Survey of iterated random functions offers a method for studying the steady state distribution of a Markov chain, and presents useful bounds on rates of convergence in a variety of examples.
We consider a discrete-Markov chain on a locally compact metric space (X, d) obtained by randomly iterating maps Ti, i ∈ IN, such that the probability pi(x) of choosing a map Ti at each step depends
• Mathematics
Bulletin of mathematical biology
• 2010
It is proved that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium.
This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a