# Random walks in random environment on trees and multiplicative chaos 1

@article{Menshikov2001RandomWI, title={Random walks in random environment on trees and multiplicative chaos 1}, author={Mikhail Menshikov and Dimitri Petritis}, journal={arXiv: Probability}, year={2001} }

We study random walks in a random environment on a regular, rooted, coloured tree. The asymptotic behaviour of the walks is classified for ergodicity/transience in terms of the geometric properties of the matrix describing the random environment. A related problem, with only one type of vertices and quite stringent conditions on the transition probabilities but on general trees has been considered previously in the literature (15). In the presentation we give here, we restrict the study of the…

## 3 Citations

### On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos

- Mathematics
- 2002

The purpose of this paper is to report on recent results concerning random walks in a random environment on monochromatic and coloured trees and their relationship with multiplicative chaos. The…

### Bindweeds or random walks in random environments on multiplexed trees and their asympotics

- MathematicsDRW
- 2003

The large time asymptotic behaviour of a new model of random walk, term the bindweed model, evolving in a random environment on an infinite multiplexed tree is studied and it is shown to coincide with the critical value of a matrix-valued multiplicative cascade on the ordinary tree.

### On pricing futures options on random binomial tree

- Mathematics, Computer Science
- 2013

A new model is developed by randomizing the environment and call such model a random binomial tree that enables calculations reflecting the real market since it consider the two states of market normal and extra ordinal.

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