Stable limits for Markov chains via the Principle of Conditioning

Autor: Mohamed El Machkouri, Dalibor Volný, Adam Jakubowski

Publikováno v: Stochastic Processes and their Applications. 130:1853-1878

We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition operator $P$ o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12feb0a91325cc32175751b495f2da78
https://doi.org/10.1016/j.spa.2019.06.002

On limit theorems for fields of martingale differences

Autor: Dalibor Volný

Publikováno v: Stochastic Processes and their Applications
Stochastic Processes and their Applications, Elsevier, 2018

We prove a central limit theorem for stationary multiple (random) fields of martingale differences f ∘ T i , i ∈ Z d , where T i is a Z d action. In most cases the multiple (random) fields of martingale differences is given by a completely commut

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23398139ff188f212d68ee2a89d87d80
https://doi.org/10.1016/j.spa.2018.03.021

Erratum to 'An invariance principle for stationary random fields under Hannan’s condition' [Stochastic Process. Appl. 124 (12) (2014) 4012–4029]

Autor: Yizao Wang, Dalibor Volný

Publikováno v: Stochastic Processes and their Applications. 127:2088-2091

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5cb5c865ada8420a0f45103fd92ee6d4
https://doi.org/10.1016/j.spa.2017.03.010

Quenched invariance principles for orthomartingale-like sequences

Autor: Magda Peligrad, Dalibor Volný

Publikováno v: Journal of Theoretical Probability
Journal of Theoretical Probability, Springer, 2019, ⟨10.1007/s10959-019-00914-z⟩

In this paper we study the central limit theorem and its functional form for random fields which are not started from their equilibrium, but rather under the measure conditioned by the past sigma field. The initial class considered is that of orthoma

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::91d4aa34707487664dd7306c7950fbb8
http://arxiv.org/abs/1802.09106

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

Autor: Dalibor Volný, Ryozo Miura, Sana Louhichi

Publikováno v: Statistics
Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2017, Special Issue in Honour of Paul Doukhan: Selected Papers from the Conference on the Occasion of Paul Doukhan’s 60th Birthday: Dependence, Limit Theorems and Applications, 51 (1), pp.167-187. ⟨10.1080/02331888.2016.1261912⟩
Statistics, 2017, Special Issue in Honour of Paul Doukhan: Selected Papers from the Conference on the Occasion of Paul Doukhan’s 60th Birthday: Dependence, Limit Theorems and Applications, 51 (1), pp.167-187. ⟨10.1080/02331888.2016.1261912⟩

International audience; The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows fro

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::043f648b6ff163fab7844d21e0c5a060
https://hal.archives-ouvertes.fr/hal-01892322