# Stochastic dynamical systems with weak contractivity properties (with a chapter featuring results of Martin Benda)

@article{Peigne2010StochasticDS, title={Stochastic dynamical systems with weak contractivity properties (with a chapter featuring results of Martin Benda)}, author={Marc Peign'e and Wolfgang Woess}, journal={arXiv: Probability}, year={2010} }

Consider a proper metric space X and a sequence of i.i.d. random continuous mappings F_n from X to X. It induces the stochastic dynamical system (SDS) X_n^x = F_n(X_{n-1}^x) starting at x in X. In this paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for…

## References

SHOWING 1-10 OF 50 REFERENCES

RANDOM DYNAMICAL SYSTEMS ON ORDERED TOPOLOGICAL SPACES

- Mathematics
- 2006

Let (Xn, n ≥ 0) be a random dynamical system and its state space be endowed with a reasonable topology. Instead of completing the structure as common by some linearity, this study stresses —…

Random difference equations and Renewal theory for products of random matrices

- Mathematics
- 1973

where Mn and Qn are random d • d matrices respectively d-vectors and Yn also is a d-vector. Throughout we take the sequence of pairs (Mn, Q~), n >/1, independently and identically distributed. The…

Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

- Mathematics
- 2008

We consider a stochastic recursion Xn+1 = Mn+1Xn + Qn+1, ($${n\in \mathbb {N}}$$), where (Qn, Mn) are i.i.d. random variables such that Qn are translations, Mn are similarities of the Euclidean space…

Conservative markov processes on a topological space

- Mathematics
- 1970

A Markov operator preservingC(X) is known to induce a decomposition of the locally compact spaceX to conservative and dissipative parts. Two notions of ergodicity are defined and the existence of…

On the absolute difference chains

- Mathematics
- 1978

Let F(x), F ( 0 ) = 0 , be a fixed probability distribution function on R § with measure F(dx), and let X 1, X 2 .. . . be a sequence of independent and identically distributed random variables with…

On invariant measures of stochastic recursions in a critical case

- Mathematics
- 2007

We consider an autoregressive model on $\mathbb{R}$ defined by the recurrence equation $X_n=A_nX_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\mathbb{R}\times\mathbb{R}^+$…

On recurrence of reflected random walk on the half-line. With an appendix on results of Martin Benda

- Mathematics
- 2006

Let $(Y_n)$ be a sequence of i.i.d. real valued random variables. Reflected random walk $(X_n)$ is defined recursively by $X_0=x \ge 0$, $X_{n+1} = |X_n - Y_{n+1}|$. In this note, we study recurrence…

On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case

- Mathematics
- 2008

We consider the autoregressive model on $\R^d$ defined by the following stochastic recursion $X_n = A_n X_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\R^d\times \R^+$.…

AN INTRODUCTION TO INFINITE ERGODIC THEORY (Mathematical Surveys and Monographs 50)

- Mathematics
- 1999

By Jon Aaronson: 284 pp., US$79.00, isbn 0 8218 0494 4 (American Mathematical Society, 1997).

Random Dynamical Systems: Theory and Applications

- Mathematics
- 2007

1. Dynamical systems 2. Markov processes 3. Random dynamical systems 4. Random dynamical systems: special structures 5. Invariant distributions: estimations and computation 6. Discounted dynamic…