Paul RAYNAUD de FITTE - RESEARCH

My research interests are mainly in Analysis and Probablity:

  • interactions of topology and geometry with probability, 
  • Young measures,
  • deterministic and stochastic differential inclusions,
  • almost periodic and almost automorphic stochastic processes,
  • stochastic dynamical systems, prey-predator systems.

 

PREPRINTS
 

  • Bedouhene (Fazia), Challali (Nouredine), Mellah (Omar), Raynaud de Fitte (Paul), and Smaali (Mannal). Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients. Preprint, February 2017 [preprint on Hal]

 

ARTICLES
 

  • Castaing (Charles), Marie (Nicolas), and Raynaud de Fitte (Paul). Sweeping processes perturbed by rough signals. Séminaire de Probabilités LI. Lecture Notes in Mathematics, vol 2301, Springer, Cham. (2022). [preprint on arXiv] [article]
  • Raynaud de Fitte (Paul). Almost periodicity and periodicity for nonautonomous random dynamical systems. Stochastics and Dynamics, Vol 21 No. 06, 2150034, 2021. [preprint on Hal] [article]
  • Marie (Nicolas) and Raynaud de Fitte (Paul). Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application. Stochastics, 93(6), 886-906, 2021 [preprint on Hal] [article]
  • Kamenskii (Mikhail), Raynaud de Fitte (Paul), Wong (Ngai-Ching), Zvereva (Margarita), A model of deformations of a discontinuous Stieltjes string with a nonlinear boundary condition, J. Nonlinear Var. Anal. 5 (2021), 737-759 [article]
  • Slimani (Safia), Raynaud de Fitte (Paul) and Boussaada (Islam). Dynamics of a prey-predator system with modified Leslie-Gower and Holling type II schemes incorporating a prey refuge. Discrete & Continuous Dynamical Systems - B, 24(9): 5003-5039, 2019. [preprint on HAL]
  • Bedouhene (Fazia), Ibaouene (Youcef), Mellah (Omar), and Raynaud de Fitte (Paul). Weyl almost periodic solutions to abstract linear and semilinear equations with Weyl almost periodic coefficients. Mathematical Methods in the Applied Sciences, 41(18): 9546–9566, 2018. [preprint on Hal]
  • Kamenskii (Mikhail), Makarenkov (Oleg), Niwanthi (Lakmi) et Raynaud de Fitte (Paul) : Global stability of almost periodic solutions of monotone sweeping processes and their response to non-monotone perturbations. Nonlinear Analysis: Hybrid Systems, 30, 213-224, 2018. [preprint on arXiv]
  • Castaing (Charles), Monteiro Marques (Manuel D. P.), Raynaud de Fitte (Paul). Second order  evolution problems with time dependent  maximal monotone  operator  and applications. In Kusuoka, Shigeo (ed.) et al., Advances in mathematical economics. Vol. 22. Springer, Singapore, 22: 25-77, 2018.
  • Castaing (Charles), Le Xuan (Truong), Raynaud de Fitte (Paul), and Salvadori (Anna). Some problems in second order evolution inclusions with boundary condition : a variational approach. In Kusuoka, Shigeo (ed.) et al., Advances in mathematical economics. Vol. 21. Springer, Singapore, 1–45, 2017.
  • Guedda (Lahcene) and Raynaud de Fitte (Paul) : Existence and Dependence Results for Semilinear Functional Stochastic Differential Equations with Infinite Delay in a Hilbert Space. Mediterr. J. Math., 13(6) :4153–4174, 2016. [article]
  • Bedouhene (Fazia), Challali (Nouredine), Mellah (Omar), Raynaud de Fitte (Paul) and Smaali (Mannal) : Almost automorphy and various extensions for stochastic processes. J. Math. Anal. Appl., 429(2):1113–1152, 2015. [preprint on HAL]
  • Kamenski (Mikhail), Mellah (Omar) and Raynaud de Fitte (Paul) : Weak averaging of semilinear stochastic differential equations with almost periodic coefficients. J. Math. Anal. Appl. 427(1):336–364, 2015. [preprint on arXiv]
  • Castaing (Charles), Godet-Thobie (Christiane), Hoang Thi (Duyen), and Raynaud de Fitte (Paul) : On the  integration of fuzzy level sets. In Kusuoka, Shigeo (ed.) et al., Advances in Mathematical Economics. Vol. 19. Tokyo : Springer. Adv. Math. Econ. 19: 1-32, 2015. [article]
  • Castaing (Charles), Monteiro Marques (Manuel D. P.), and Raynaud de Fitte (Paul) : Some problems in optimal control governed by the sweeping process. J. Nonlinear Convex Anal., 15(5):1043–1070, 2014. [article]
  • Bouchemella (Nadira) and Raynaud de Fitte (Paul) : Weak solutions of backward stochastic differential equations with continuous generator. Stochastic Process. Appl., 124(1):927–960, 2014. [preprint on HAL]
  • Mellah (Omar) and Raynaud de Fitte (Paul) : Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients. Electron. J. Differential Equations (2013), No. 91, 7 pp.(electronic). [article]
  • Castaing (Charles) and Raynaud de Fitte (Paul) : Law of large numbers and ergodic theorem for convex weak-star compact valued Gelfand-integrable mappings. In Kusuoka, Shigeo (ed.) et al., Advances in Mathematical Economics. Vol. 17. Tokyo : Springer. Adv. Math. Econ. 17: 1-37, 2013. [preprint]
  • Bedouhene (Fazia), Mellah (Omar), and Raynaud de Fitte (Paul) : Bochner-almost periodicity for stochastic processes. Stoch. Anal. Appl., 30(2):322-342, 2012. [preprint on HAL]
  • Dedecker (Jérôme), Prieur (Clémentine), and Raynaud de Fitte (Paul). Parametrized Kantorovich-Rubinštein Theorem and application to the coupling of random variables. In Dependence in Probability and Statistics, volume 187 de Lecture Notes in Statistics, pages 105-121. Springer, New York, 2006. [preprint on arXiv]
  • Castaing (Charles), Raynaud de Fitte (Paul), and Salvadori (Anna). Some variational convergence results with applications to evolution inclusions. In Kusuoka, Shigeo (ed.) et al., Advances in mathematical economics. Vol. 8. 2006. Tokyo: Springer. Adv. Math. Econ.  8, 33-73, 2006. [article]
  • Castaing (Charles), Raynaud de Fitte (Paul), and Salvadori (Anna). Some variational convergence results for a class of evolution inclusions of second order using Young measures. In Kusuoka, Shigeo (ed.) et al., Advances in mathematical economics. Vol. 7. Tokyo: Springer. Adv. Math. Econ. 7, 1-32, 2005. [article]
  • Raynaud de Fitte (Paul). Compactness criteria for the stable topology. Bull. Pol. Acad. Sci., Math., 51(4):343--363, 2003. [article]
  • Castaing (Charles) and Raynaud de Fitte (Paul). On the fiber product of Young measures with application to a control problem with measures. In Kusuoka, Shigeo (ed.) et al., Advances in mathematical economics. Vol. 6. Tokyo: Springer. Adv. Math. Econ. 6, 1-38. 2004. [article]
  • Jakubowski (Adam), Kwapień (Stanisław), Raynaud de Fitte (Paul), and Rosiński (Jan). Radonification of cylindrical semimartingales by a single Hilbert-Schmidt operator. Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP), 5(3):429--441, 2002. [article]
  • Raynaud de Fitte (Paul) and Zięba (Wiesław). On the construction of a stable sequence with given density. Ann. Univ. Mariae Curie-Skłodowska Sect. A, 56(8):77--84, 2002. [link to the journal]
  • Castaing (Charles) and Raynaud de Fitte (Paul). S--Uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space. J. Theor. Probab., 13(1):93--134, 2000. [preprint]
  • Raynaud de Fitte (Paul). Théorème ergodique ponctuel et lois fortes des grands nombres pour des points aléatoires d'un espace métrique à courbure négative. The Annals of Probability, 25(2):738--766, 1997. [article]

 

MONOGRAPH

 

  • Castaing (Charles), Raynaud de Fitte (Paul), and Valadier (Michel). Young measures on Topological Spaces. With Applications in Control Theory and Probability Theory, volume 571 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 2004. [book]   [erratum]

 

SEMINAR PAPERS

 

  • Raynaud de Fitte (Paul). Deux lois fortes des grands nombres pour des ensembles aléatoires. Sém. Anal. Convexe, 21:1.1-1.28, 1991.
  • Raynaud de Fitte (Paul). Loi forte des grands nombres de Padgett et Taylor pour des ensembles aléatoires. In Séminaire de Mathématiques de Rouen, Compte Rendu des Séances Oct. 90 - Juin 91, pages 91-98. Publications de l'Université de Rouen numéro 183, 1991.

 

HABILITATION A DIRIGER DES RECHERCHES

  • Raynaud de Fitte (Paul). Autour de la notion de mesure. Synthesis work for the french "habilitation à diriger des recherches", December 2004. [HAL]

 

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