Welcome to Miguel Martinez's home page !

Contact

miguel.martinez@u-pem.fr


Mail Adress:
Laboratoire d'Analyse et de Mathematiques Appliquees
LAMA UMR 8050
Universite de Marne-la-Vallee
5, boulevard Descartes
Cite Descartes - Champs-sur-Marne
77454 Marne-la-Vallee cedex 2
France
Phone: +33 (0) 1 60 95 75 25


How differentiation was born...
(drawing by Quino)

Current situation

I am Maitre de Conference at the University Paris-Est Marne-la-Vallee since september 2007.

Publications

1. Denis, Christophe ; Dion, Charlotte ; Martinez, Miguel
   Consistent procedures for multiclass classification of diffusion paths
   Scand. J. Statist. (2019) 1-39


2. Gloter, Arnaud ; Martinez, Miguel
   Bouncing Skew Brownian Motions
   J. Theoret. Probab. 31 (2018), no. 1, 319-363


3. Etore, Pierre ; Martinez, Miguel
   Time inhomogeneous Stochastic Differential Equations invloving the local time of the unknown process, and associated parabolic operators
   Stochastic Processes and their Applications, published online in October 2017


4. Goreac, Dan ; Kobylanski, Magdalena ; Martinez, Miguel
   A piecewise deterministic Markov toy model for traffic/maintenance and associated Hamilton-Jacobi integrodifferential systems on networks
   Appl. Math. Optim. 74 (2016), no. 2, 375-421.


5. Goreac, Dan ; Martinez, Miguel
   Algebraic invariance conditions in the study of approximate (null-)controllability of Markov switch processes
   Math. Control Signals Systems 27 (2015), no. 4, 551-578.


6. Etore, Pierre ; Martinez, Miguel
   Exact simulation for solutions of one-dimensional stochastic differential equations with discontinuous drift
   ESAIM P&S, October 2014, Vol. 18, pp 686-702


7. Etore, Pierre ; Martinez, Miguel
   Exact simulation of one-dimensional stochastic differential involving the local time of the unknown process
   Monte-Carlo Methods and Applications, Vol 19(1) pp. 41-71 (2013)


8. Gloter, Arnaud; Martinez, Miguel
   Distance between two skew Brownian motions as a SDE with jumps and law of the hitting time
   Annals of Probability, (2012)


9. Etore, Pierre; Martinez, Miguel
   On the existence of a time inhomogeneous skew Brownian motion and some related laws
   Electronic Journal of Probability, (2012)


10. Martinez, Miguel; Talay, Denis
    One-Dimensional Parabolic Diffraction Equations: Pointwise Estimates and Discretization of Related Stochastic Differential Equations With Weighted Local Times
    Electronic Journal of Probability, (2012)


11. Martinez, Miguel; San Martin, Jaime; Torres, Soledad
    Numerical method for Reflected Backward Stochastic Differential Equations
    Stochastic Analysis and Applications (2011)


12. Bardou, Olivier; Martinez, Miguel
    Statistical estimation for reflected skew processes
    Stat. Inference Stoch. Processes 13, (2010), 231:248


13. Bernardin, Frederic; Bossy, Mireille; Martinez, Miguel; Talay, Denis
    On mean discounted numbers of passage times in small balls of Ito processes observed at discrete times
    Elec. Comm. Prob. 14, (2009), 302-316


14. Martinez, Miguel; Rubenthaler, Sylvain; Tanre, Etienne
    Approximations of a Continuous Time Filter. Application to Optimal Allocation Problems in Finance
    Stochastic Analysis and Applications vol. 27, (2009), no. 2, 270-296
    


15. Fontbona, Joaquin; Martinez, Miguel
    Paths clustering and an existence result for stochastic vortex systems
    J. Stat. Phys. 128 (2007), no. 3, 699--719
    


16. Lejay, Antoine; Martinez, Miguel
    A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients
    Ann. Appl. Probab. 16 (2006), no. 1, 107--139
    


17. Martinez, Miguel; Talay, Denis
    Discretisation d'equations differentielles stochastiques unidimensionnelles et generateur sous forme divergence avec coefficient discontinu
    C.R. Math. Acad. Sci. Paris 342 (2006), no. 1, 51-56
    

With J.P. Lepeltier : unpublished note Dynkin games and RBSDEs (available on demand)

PhD

My PhD supervisor was Pr. Denis TALAY.

I have defended my PhD on the 18th of May 2004 in front of the following jury:


Denis Talay, Director of Research of the TOSCA research team, Professor at the Ecole Polytechnique, France. PhD supervisor.
Alexander Veretennikov, Professor at the University of Leeds, Great Britain. Referee.
Dominique Lepingle, Professor at the University of Orleans, France. Referee.
Gilles Pages, Professeur at University of Paris 6, Pierre et Marie Curie. President.
Etienne Pardoux, Professor at University of Provence, France. Member.


My PhD manuscript is available here.

Working group ASPro

Together with P.M. Samson and M. Hebiri, I am an organizer of the working group groupe de travail probabilites, statistiques et applications (ASPRo) which takes place (almost) every tuesday mornings at the UPMLV. Please send me an e-mail if you wish to receive the invitations of this working group.