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Welcome to Miguel Martinez's home page !


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Current situation

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



Publications

  1. Gloter Arnaud ; Martinez, Miguel
    Bouncing Skew Brownian Motions

    J. Theoret. Probab. 31 (2018), no. 1, 319-363

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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)

  7. 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)

  8. Etore, Pierre; Martinez, Miguel
    On the existence of a time inhomogeneous skew Brownian motion and some related laws

    Electronic Journal of Probability, (2012)

  9. 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)

  10. Martinez, Miguel; San Martin, Jaime; Torres, Soledad
    Numerical method for Reflected Backward Stochastic Differential Equations

    Stochastic Analysis and Applications (2011)

  11. Bardou, Olivier; Martinez, Miguel
    Statistical estimation for reflected skew processes

    Stat. Inference Stoch. Processes 13, (2010), 231:248

  12. 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

  13. 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

  14. Fontbona, Joaquin; Martinez, Miguel
    Paths clustering and an existence result for stochastic vortex systems

    J. Stat. Phys. 128 (2007), no. 3, 699--719

  15. Lejay, Antoine; Martinez, Miguel
    A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

    Ann. Appl. Probab. 16 (2006), no. 1, 107--139

  16. 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


Working group ASPro

Together with P.M. Samson and M. Hebiri, I am an organizer of the working group groupe de travail probabilit?s, 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.