Research

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Preprints

  .  A stochastic model for speculative bubbles.

     With Sebastien Gadat and Laurent Miclo. arXiv

. Ergodicity of SDEs driven by fractional Brownian motion with multiplicative noise.

With Joaquin Fontbona. HAL

 

 

Publications

    . Invariant distribution of duplicated diffusions and application to Richardson-Romberg extrapolation.

     With Vincent Lemaire and Gilles Pages. To appear in Annales de l’IHP(B). HAL

    . Approximation of stationary solutions to SDEs driven by multiplicative fractional noise. .

With Serge Cohen and Samy Tindel. Stochastic Processes and Applications. Volume 124 (3). 2014. 1197-1225. HAL

    . A mixed-step algorithm for the approximation of the stationary regime of a diffusion

With Gilles Pages. Stochastic Processes and Applications. Volume 124 (1). 2014. 522-565. HAL

. Long Time Behavior of and Stationary Regime of Memory Gradient Diffusions.

With  Sebastien Gadat. Annales de l’IHP(B). Volume 50 (2). 2014. 564-601. HAL

    . Large Deviation Principle for invariant distributions of Memory Gradient Diffusions.

With  Sebastien Gadat and Clement Pellegrini.  EJP. Volume 18 (81). 2013. 1-34. HAL

      . Ergodic Approximation of the distribution of a stationary diffusion: Rate of convergence.

 

    With Gilles Pages. Annals of Applied Probability. Volume 22 (3). 2012. 1059-1100.  HAL

 

    . Approximation of Stationary Solutions of Gaussian Driven Stochastic Differential Equations.

 

   With Serge Cohen. Stochastic Processes and Applications. 121 (12). 2011. 2776-2801. HAL

 

   . Estimation of the instantaneous volatility.

                 

   With Alexander Alvarez, Monique Pontier and Nicolas Savy. Statistical Inference for Stochastic Processes.

   Volume 15 (1) 2012. 27-59. Arxiv

 

   . A connection between extreme value theory and long time Approximation of SDEs.

 

   Stochastic processes and their applications. 19 (10). 2009. 3583-3607. HAL

 

  . Approximation of the distribution of a stationary Markov process with application to option pricing.

 

  With Gilles Pages. Bernoulli. 15 (1). 2009. 146-177. HAL

 

  . Computation of the invariant measure of a Levy driven SDE: Rate of convergence.

 

  Stochastic processes and Applications. 118 (8). 2008. HAL

 

 . Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process.

 

 Annals of Applied Probability. 18 (2). 2008. HAL

 

Works in progress

 

. With Sébastien Gadat and Sofiane Saadane : Regret bounds for Narendra-Shapiro bandit algorithms (finalization).  

 

. With Michel Benaim and Bertrand Cloez : A stochastic approximation approach for quasi-stationary distributions of diffusions (in progress)

 

. With Vincent Lemaire and Gilles Pagès : A Multilevel-Romberg algorithm for the approximation of stationary distributions of diffusions.

 

. With Bruno Saussereau and Samy Tindel : Estimation of the drift for fractional diffusions.

 

PHD Students

. 2013- Sofiane Saadane (supervised with Sébastien Gadat).  Topics : Stochastic Algorithms, PDMPs.

PHD Thesis

Approximation du regime stationnaire d'une EDS avec sauts".

Supervisor : Gilles Pages (Universite Paris-VI).

Thesis defense : 13/12/2006.