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Welcome to Miguel Martinez's home page !


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Current situation

I am Maitre de Conference (HDR) at the Universite Gustave Eiffel since september 2008.



Publications

  1. Bonnetier, Eric ; Etore Pierre ; Martinez, Miguel
    A probabilistic representation of the solution to a 1D evolution equation in a medium with negative index
    To appear in Journal of Statistical Physics (2025).

  2. Martinez, Miguel; Ohavi Isaac
    Martingale problem for a Walsh spider process with spinning measure selected from its own local time
    Electron. J. Probab. 30 (2025), article no. 22, 1–39.

  3. Martinez, Miguel; Ohavi Isaac
    Well posedness of linear parabolic partial differential equations posed on a star-shaped network with local time Kirchhoff's boundary condition at the vertex
    J. Math. Anal. Appl. 537 (2024), no. 2, Paper No. 128294, 49 pp.

  4. Etore, Pierre; Martinez, Miguel
    Stochastic processes associated to multidimensional parabolic transmission problems in divergence form
    ALEA Lat. Am. J. Probab. Math. Stat. 20 (2023), no. 1, 291–311.

  5. Denis, Christophe; Dion-Blanc, Charlotte; Martinez, Miguel
    A ridge estimator of the drift from discrete repeated observations of the solution of a stochastic differential equation
    Bernoulli 27 (2021), no. 4, 2675–2713.

  6. Etore, Pierre; Martinez, Miguel
    A transformed stochastic Euler scheme for multidimensional transmission PDE
    J. Comput. Appl. Math. 394 (2021), Paper No. 113551, 28 pp.

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

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

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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)

  14. 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)

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

  16. 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)

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

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

  19. 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

  20. 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

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

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

  23. 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


Proposition de sujet de these pour le projet MathPhdInFrance COFUND



Research notes

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

HdR


PhD