# General erased-word processes: Product-type filtrations, ergodic laws and Martin boundaries

@article{Gerstenberg2017GeneralEP, title={General erased-word processes: Product-type filtrations, ergodic laws and Martin boundaries}, author={Julian Gerstenberg}, journal={Stochastic Processes and their Applications}, year={2017} }

## 3 Citations

### Exchangeable interval hypergraphs and limits of ordered discrete structures

- MathematicsThe Annals of Probability
- 2020

A hypergraph $(V,E)$ is called an interval hypergraph if there exists a linear order $l$ on $V$ such that every edge $e\in E$ is an interval w.r.t. $l$; we also assume that $\{j\}\in E$ for every…

### Exchangeable Laws in Borel Data Structures

- Mathematics
- 2022

. Motivated by statistical practice, category theory terminology is used to introduce Borel data structures and study exchangeability in an abstract framework. A generalization of de Finetti’s…

### Empirical process of concomitants for partly categorial data and applications in statistics

- MathematicsBernoulli
- 2022

On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called…

## 22 References

### Filtrations of the Erased-Word Processes

- Computer Science
- 2016

It is shown that the poly-adic filtration generated by such a process is standard and constructed with the help of Vershik's theory of filtrations in discrete negative time.

### DOOB-MARTIN COMPACTIFICATION OF A MARKOV CHAIN FOR GROWING RANDOM WORDS SEQUENTIALLY.

- MathematicsStochastic processes and their applications
- 2017

### Doob--Martin boundary of R\'emy's tree growth chain

- Mathematics
- 2014

R\'emy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the $n^{\mathrm{th}}$ tree is uniformly distributed over the set of rooted, planar,…

### The filtration of the split-words process

- Mathematics
- 2011

Smorodinsky and Laurent have initiated the study of the filtrations of split-word processes, in the framework of discrete negative time. For these filtrations, we show that Laurent’s sufficient…

### Exchangeable interval hypergraphs and limits of ordered discrete structures

- MathematicsThe Annals of Probability
- 2020

A hypergraph $(V,E)$ is called an interval hypergraph if there exists a linear order $l$ on $V$ such that every edge $e\in E$ is an interval w.r.t. $l$; we also assume that $\{j\}\in E$ for every…

### Vershik’s Intermediate Level Standardness Criterion and the Scale of an Automorphism

- Mathematics
- 2013

In the case of r n -adic filtrations, Vershik’s standardness criterion takes a particular form, hereafter called Vershik’s intermediate level criterion. This criterion, whose nature is combinatorial,…

### On exchangeable random variables and the statistics of large graphs and hypergraphs

- Mathematics
- 2008

De Finetti’s classical result of [18] identifying the law of an
exchangeable family of random variables as a mixture of i.i.d. laws was
extended to structure theorems for more complex notions of…

### Poly-adic filtrations, standardness, complementability and maximality

- Mathematics
- 2017

Etant donn{e}e une filtration $(\zc_n)_{n \le 0}$ index{e}e par les entiers n{e}gatifs, nous introduisons la notion de compl{e}mentabilit{e} pour les filtrations incluses dans $(\zc_n)_{n \le 0}$.…

### Radix sort trees in the large

- Computer Science
- 2016

This work investigates the tree-valued Markov chains that arise when successively storing infinite binary strings and characterizes all the ways that it is possible to condition such a chain of radix sort trees consistently on its behavior "in the large".