Prof. Martial Longla
Mathematics, University of Mississippi, Oxford, Alabama, USA
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Academic Career Length
15Years (2012-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications1 October 2012 in Journal of Multivariate Analysis
Journal Article
Martial LonglaMPMagda Peligrad
Magda Peligrad
10 October 2014 in ESAIM: Probability and Statistics
Journal Article
Martial LonglaWe consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential ρ-mixing. We analyse the example of the Mardia and Frechet copula families using small sets.
10 June 2021 in Journal of the Korean Statistical Society
Journal Article
Martial LonglaFNFidel Djongreba Ndikwa
Fidel Djongreba NdikwaMMMathias Nthiani Muia
Mathias Nthiani MuiaPTPatrice Soh Takam
Patrice Soh Takam24 June 2022 in Journal of Statistical Theory and Applications
Journal Article
Martial LonglaHMHamadou Mous-Abou
Hamadou Mous-AbouINIsidore Seraphin Ngongo
Isidore Seraphin NgongoThis paper brings some insights of $$\psi '$$ -mixing, $$\psi ^*$$ -mixing and $$\psi$$ -mixing for copula-based Markov chains and the perturbations of their copulas. We provide new tools to check Markov chains for $$\psi$$ -mixing or $$\psi '$$ -mixing. We show that perturbations of $$\psi '$$ -mixing copula-based Markov chains are $$\psi '$$ -mixing while perturbations of $$\psi$$ -mixing Markov chains are not necessarily $$\psi$$ -mixing Markov chains, even when the perturbed copula generates $$\psi$$ -mixing. The Farlie–Gumbel–Morgenstern, gaussian and Ali-Mikhail-Haq copula families are considered among other examples. A statistical study is provided to emphasize the impact of perturbations on copula-based Markov chains in a simulation study. Moreover, we provide a correction to a statement made in Longla et al. (J Korean Stat Soc, 1–23, 2021) on $$\psi$$ -mixing.
About Me
Dr. Longla was born in 1978 in Mbouda, small city in the west Province of Cameroon. He spent 6 years at the public primary school "Ecole Publique Bamessingue Ville", then 7 years at the public high school "Lycee Bilingue de Mbouda" from which he graduated valedictorian in 1997. After a year at the University of Yaounde I, Dr. Longla was awarded a scholarship to further his education in Russia. Dr. Longla received several diplomas at the Peoples' Friendship University of Russia: Teacher of Russian as foreign Language, interpreter/translator with 3 languages (French, Russian, English) with honors, Bachelor of Sciences and Master of sciences in Mathematics, and several University and city awards for his leadership in the fight for students rights and promotion of African culture. Dr. Longla also performed as comedian with some of the most popular Russian artists. Dr. Longla completed a PhD program in Moscow on Optimal control problems in infinite dimensional spaces in 2008 and moved to the University of Cincinnati where he engaged in a PhD program in Probability and Statistics. Dr. Longla received a Master of Sciences in Statistics in 2010 and a PhD in mathematics in 2013. His dissertation was on "Modelling dependence and limit theorems for copula-based Markov chains". Dr Longla has been supported by the NSF (through his adviser Dr. Madga Peligrad), The Laws fellowship, the University Research council and the Taft center at the University of Cincinnati.
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