• 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}
}
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

Locally contracting iterated functions and stability of Markov chains

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

Invariant Probabilities of Markov-Feller Operators and Their Supports

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

An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

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

Practical drift conditions for subgeometric rates of convergence

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

Invariant measures for Markov processes arising from iterated function systems with place-dependent

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

Iterated Random Functions

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.

Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator

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

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

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.

Probability: Theory and Examples

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