Conditioned local limit theorems for random walks defined on finite Markov chains

Autor: Ronan Lauvergnat, Emile Le Page, Ion Grama

Publikováno v: Probability Theory and Related Fields
Probability Theory and Related Fields, Springer Verlag, 2020, 176 (1-2), pp.669-735. ⟨10.1007/s00440-019-00948-8⟩

Let $$(X_n)_{n\geqslant 0}$$ be a Markov chain with values in a finite state space $${\mathbb {X}}$$ starting at $$X_0=x \in {\mathbb {X}}$$ and let f be a real function defined on $${\mathbb {X}}$$. Set $$S_n=\sum _{k=1}^{n} f(X_k)$$, $$n\geqslant 1

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7117e4b77fdfcaa9fe20d7c084f0c165
https://hal.archives-ouvertes.fr/hal-02878963/document

Limit theorems for affine Markov walks conditioned to stay positive

Autor: Emile Le Page, Ion Grama, Ronan Lauvergnat

Publikováno v: Ann. Inst. H. Poincaré Probab. Statist. 54, no. 1 (2018), 529-568
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2018, 54 (1), pp.529-568
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2018, 54 (1), pp.529-568. ⟨10.1214/16-AIHP814⟩

International audience; Consider the real Markov walk $S_n = X_1+ \dots+ X_n$ with increments $\left(X_n\right)_{n\geqslant 1}$ defined by a stochastic recursion starting at $X_0=x$. For a starting point $y>0$ denote by $\tau_y$ the exit time of the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9571c70034a828960d835024f732a8ab
https://projecteuclid.org/euclid.aihp/1519030838

On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Autor: Ion Grama, Marc Peigné, Emile Le Page

Publikováno v: Colloquium Mathematicum
Colloquium Mathematicum, 2014, 134 (1), pp.1-55

International audience; We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc1fbf1571526ed1e9eff1e07f3bc9be
https://doi.org/10.4064/cm134-1-1

The survival probability of a critical branching process in a Markovian random environment

Autor: Emile Le Page, Yinna Ye

Publikováno v: Comptes Rendus Mathematique. 348:301-304

In this Note, we first prove a local limit theorem for a semi-Markov chain and then apply it to study the asymptotic behavior of the survival probability of a critical branching process in Markovian random environment.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::39f1c85564e28bbc33cd400a83d099de
https://doi.org/10.1016/j.crma.2010.01.014

On the multidimensional stochastic equation

Autor: Emile Le Page, Benoîte de Saporta, Yves Guivarc'h

Publikováno v: Comptes Rendus Mathematique. 339:499-502

We study the behavior at infinity of the tail of the stationary solution of a multidimensional linear auto-regressive process with random coefficients. We exhibit an extended class of multiplicative coefficients satisfying a condition of irreducibili

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0d1a80e3db7b28718e6cf86fd7d1e6f6
https://doi.org/10.1016/j.crma.2004.07.024