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Publications and Thesis of Dr. Larbi Alili

Articles

  1. Space and time inversions of stochastic processes and Kelvin transform, with L. Chaumont, P. Graczyk and T. Żak, Mathematische Nachrichten, 292, no 2, 251-272, 2019.
  2. On the semi-group of a scaled skew Bessel process, with A. Aylwin, Statistics & Probability letters, 145, 96-102, 2019.
  3. Further studies on square-root boundaries of Bessel processes, with H. Matsumoto, Electron. Commun. Probab., 23, no. 39, 2018.
  4. Inversion, duality and Doob h-transforms for self-similar Markov processes, with L. Chaumont, P. Graczyk and T. Żak, Electron. J. Probab., 22, no. 20, 1-18, 2017.
  5. On inversions and Doob h-transforms of linear diffusions, with P. Graczyk and T. Zak, Séminaire de Probabilités XLVII, volume In Memoriam Marc Yor, 2015.
  6. On exponential functionals, harmonic potential measures and undershoots of subordinators, with W. Jedidi and V. Rivero, ALEA, Lat. Am. J. Probab. Math. Stat. 11 (2), 711-735, 2014.
  7. Boundary-crossing identities for Brownian motion and some nonlinear ode’s, with P. Patie, Proc. Amer. Math. Soc. 142, 3811-3824, 2014.
  8. Müntz Linear transforms of Brownian motion, with C-T Wu, Electron. J. Probab. 19 , no. 36, 1–15, 2014.
  9. Boundary crossing identities for self-similar diffusions having the time inversion property, with P. Patie, J. Theoret. Prob. 23, no. 1, 65-84, 2010.
  10. Further results on some singular linear stochastic differential equations, with C-T Wu, Stochastic Processes and their Applications, 2009.
  11. On the joint law of the L1 and L2 norms of a 3-dimensional Bessel bridge, with P. Patie. Sem. de Prob., XL, Springer, Berlin, pp. 247-264, 2007.
  12. Representations of the first hitting time density of an Ornstein-Uhlenbeck process, with J.L. Pedersen and P. Patie, Stoch. Mod., Vol. 21, Part 4, 2005
  13. On the first crossing times of a Brownian motion and a family of continuous curves, with P. Patie. C. R. Acad. Sci. Paris, Sér. I 340, pp. 225-228, 2005
  14. On a fluctuation identity for random walks and Lévy processes, with L. Chaumont and R.A. Doney, Bull. Lond. Math. Soc, Vol. 37, Part1, pp. 141-148, 2005
  15. Some remarks on first passage of Lévy processes, the American put option and pasting principals, with A. Kyprianou, Ann. Appl. Prob., Vol. 15, No 3, pp. 2062-2080, 2005
  16. Canonical decomposition of certain generalized Brownian bridges, ECP, Vol. 7, Paper number 3, pp. 27--35, 2002
  17. On a triplet of exponential Wiener functionals, with H. Matsumoto and T. Shiraishi, Sem. de Prob. XXXV, Springer, Berlin, pp. 396-415, 2001
  18. On some new fluctuation identities for Lévy processes, with L. Chaumont, Bernoulli 7 (3), pp. 557--569, 2001
  19. Martin Boundaries associated with a killed random walk, with R.A. Doney, Ann. I. H. P., Vol. 37, N. 3, 313-338, 2001
  20. Quelques nouvelles identités de fluctuations pour les processus de Lévy, with L. Chaumont, C. R. Acad. Sci. Paris, t. 328, Sér. I 328, pp. 613-616, 1999
  21. Wiener-Hopf factorization revisited and some applications, with R.A. Doney, Stochastics and stochastics reports, 66, pp. 87-102, 1999
  22. On some hyperbolic principal values of Brownian Motion. In "Exponential functionals and principal values related to Brownian Motion", Biblioteca de la Revista Matemảtica Ibero-Americana, Editor Marc Yor, 1997.
  23. Une identité en loi remarquable pour l’excursion brownienne normalisée, with C.D. Martin and M. Yor. In "Exponential functionals and principal values related to Brownian Motion", Biblioteca de la Revista Matemảtica Ibero-Americana, Editor Marc Yor, 1997.
  24. Sur l'identité de Bougerol pour les fonctionnelles exponentielles du mouvement brownien avec drift, with D. Dufresne and M. Yor. In "Exponential functionals and principal values related to Brownian Motion", Biblioteca de la Revista Matemảtica Ibero-Americana, Editor Marc Yor, 1997.
  25. An explanation of a generalized Bougerol's identity in terms of hyperbolic geometry, with J. C. Gruet. In "Exponential functionals and principal values related to Brownian Motion", Biblioteca de la Revista Matemảtica Ibero-Americana, Editor Marc Yor, 1997.

Ph. D. Thesis

  1. Fonctionnelles exponentielles et certaines valeurs principales des temps locaux browniens. Thèse de Doctorat de l’université Paris VI, 1995. Supervised by Marc Yor.

Work in Progress and Preprints

  1. A characterisation of linear self-similar Markov processes having the time inversion property, with A. Aylwin.