Patie, Pierre Bernard

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Patie, Pierre (2009). Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes. Annales de l'Institut Henri Poincaré - probabilités et statistiques, 45(3), pp. 667-684. Bethesda, Md.: Association des Publications de l'Institut Henri Poincaré 10.1214/08-AIHP182

Patie, Pierre (2009). A few remarks on the supremum of stable processes. Statistics & probability letters, 79(8), pp. 1125-1128. Amsterdam: North-Holland 10.1016/j.spl.2009.01.001

Patie, Pierre (2009). Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration. Bulletin des sciences mathématiques, 133(4), pp. 355-382. Paris: Gauthier-Villars 10.1016/j.bulsci.2008.10.001

Patie, Pierre (2009). Law of the exponential functional of one-sided Lévy processes and Asian options. Loi de la fonctionnelle exponentielle de processus de Lévy assymétriques et options asiatiques. Comptes rendus - mathématique, 347(7-8), pp. 407-411. Paris: Elsevier Masson SAS 10.1016/j.crma.2009.02.013


Patie, Pierre; Winter, Christoph (2008). First exit time probability for multidimensional diffusions: A PDE-based approach. Journal of computational and applied mathematics, 222(1), pp. 42-53. Antwerp: North-Holland 10.1016/

Patie, Pierre (2008). q-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup. Alea -Latin American journal of probability and mathematical statistics, 4, pp. 31-43. Beachwood, Ohio: Institute of Mathematical Statistics


Patie, Pierre (2007). Two-sided exit problem for a spectrally negative alpha-stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions. Electronic communications in probability, 12, pp. 146-160. Shaker Heights, Ohio: Institute of Mathematical Statistics

Alili, Larbi; Patie, Pierre (2007). On the Joint Law of the L1 and L2 Norms of a 3-Dimensional Bessel Bridge. In: Donati-Martin, Catherine; Émery, Michel; Rouault, Alain; Stricker, Christophe (eds.) Séminaire de Probabilités XL. Lecture Notes in Mathematics: Vol. 1899 (pp. 247-264). Heidelberg: Springer Verlag

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