Paul Doukhan is one of the most influential researchers in the areas of dependence and limit theorems for stochastic processes. His friends, students and colleagues from around the globe gathered at the Institut Henri Poincaré, Paris, in May 2015 in order to participate in a conference honouring him on the occasion of his 60th birthday. This volume is dedicated to Paul and consists of papers which were contributed by his friends and collaborators, including several of those that were presented during the conference.
Paul was born in Algeria but left the country and moved to France in a very young age, much before Algeria declared its independence. Being one year younger than it was usual for pupils to start schooling, he started his secondary education by joining an elite class of young and brilliant classmates of his age or younger. However, because he faced difficulties in the Latin language, he had to join a lower-level class. In fact, in his third year of his studies he even had to repeat the last year of middle school. Then, in high school, he was attracted to the study of economics. At the same time, there was a change in the educational programmes. In particular, modern mathematics, including set theory, were introduced in the curriculum. In addition, his economics professor encouraged him to move towards mathematics, where he was very successful.
In 1975, Paul joined the Ecole Normale Supérieure in Saint Cloud and he defended his Ph.D. thesis, which he completed in 1981 under the supervision of Jean Bretagnolle, who sadly passed away last summer. It should be noted that this school is now in Lyon. Paul was successful in gaining ‘agrégation de mathématiques’ ranked as 11th. This particular scientific development was interesting enough to be noticed and reported by the satirical journal Le Canard Enchaîné.
Paul's first position was at Rouen University. This was followed by a research position at CNRS between 1983 and 1993. Additionally, he spent one year lecturing and researching in China. Since 1993, Paul is professor at the University Cergy-Pontoise where, since 2009, he holds an ‘exceptional professorial rank’. Additionally, he was a member of ENSAE from 2002 to 2008 working mostly on applications in econometrics and, at the same time, he had a strong involvement in the French high-school professors selection procedure (agrégation). Furthermore, in 2011, he was successful in obtaining a position at IUF (Institut Universitaire de France) as a Senior member, which is one step before being elected to the French Academy of Sciences.
Paul's work is mainly theoretical and involves the derivation of procedures for obtaining dependence conditions and studying the asymptotic properties of stochastic processes models. The main tools that he had used for this purpose are, especially, those of analysis, but also those of harmonic analysis, probability theory, algebra and combinatorics.
Paul started his research work by organizing the existing knowledge of the notions of mixing (see [Citation1]). He reinforced the probabilistic and statistical limit theory in the context of stationary and mixing sequences. All this work is reported in Doukhan [Citation2]. This volume provides a state-of-the-art reference for the probabilistic results related to the notions of mixing, including moment and exponential inequalities as well as several maximal inequalities and examples of mixing random processes. This monograph has become very popular and has been cited extremely frequently in the literature. However, it is well known that mixing cannot be employed for studying properties of autoregressive models with discrete innovations (see [Citation3]). In the paper by Doukhan and Louhichi [Citation4], written with one of his brilliant doctoral students, Sana Louhichi, the authors introduce the notion of weak dependence, a concept which is well suited for use by practitioners, because it provides naturally sufficient dependence conditions for obtaining asymptotic results.
Paul has several other research interests and has made influential contributions in the areas of long-range dependence, extreme value theory and empirical processes. He is collaborating continuously with several researchers around the world. Currently, he is active in new areas of research such as non-stationary time series, random fields, point processes and random matrices. He is also involved in applied problems from the fields of environmetrics, biology and actuarial sciences.
In addition to his influential research, Paul has provided tremendous service to the profession. He has produced several brilliant students in the field (notably Ph. Soulier, C. Prieur, S. Louhichi, O. Wintenberger, among others), he supervised post-doctoral researchers and he was the main organizer of many high calibre scientific events. He has also contributed to the success of the LABEX MME-DII (an important research grant funded by the French government).
We wish Paul all the best for a long and healthy life as well as for the continuation of his vibrant research activities for many years to come.
References
- Rosenblatt M. A central limit theorem and a strong mixing condition. Proc Natl Acad Sci USA. 1956;42:43–47. doi: 10.1073/pnas.42.1.43
- Doukhan P. Mixing: properties and examples. Lecture Notes in Statistics Vol. 85, New York: Springer; 1994.
- Andrews D. Non-strong mixing autoregressive processes. J Appl Probab. 1984;21:930–934. doi: 10.1017/S0021900200037633
- Doukhan P., Louhichi S. A new weak dependence condition and applications to moment inequalities. Stoch Process Appl. 1999;84:313–342. doi: 10.1016/S0304-4149(99)00055-1