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".