no. 11
Probability Theory
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
[Une classe d'équations différentielles stochastiques à coefficients non lipschitziens : unicité forte et non explosion]

Présenté par : Paul Malliavin

Fang, Shizan1 ; Zhang, Tusheng2
1 I.M.B, UFR sciences et techniques, Université de Bourgogne, 9, avenue Alain Savary, BP 47870, 21078 Dijon, France
2 Department of Mathematics, University of Manchester, Oxford road, Manchester, M13 9PL, UK
Comptes Rendus. Mathématique, Tome 337 (2003) no. 11, pp. 737-740.

La condition lipschitzienne locale sera affaiblie dans l'établissemnt de l'unicité trajectorielle d'une e.d.s ; de plus, nous montrerons que la solution a un temps de vie infini sous la croissance ξlogξ.

A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.10.008
Fang, Shizan 1 ; Zhang, Tusheng 2

1 I.M.B, UFR sciences et techniques, Université de Bourgogne, 9, avenue Alain Savary, BP 47870, 21078 Dijon, France
2 Department of Mathematics, University of Manchester, Oxford road, Manchester, M13 9PL, UK 
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Fang, Shizan; Zhang, Tusheng. A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion. Comptes Rendus. Mathématique, Tome 337 (2003) no. 11, pp. 737-740. doi : 10.1016/j.crma.2003.10.008. http://archive.numdam.org/articles/10.1016/j.crma.2003.10.008/

[1] Fang, S. Canonical Brownian motion on the diffeomorphism group of the circle, J. Funct. Anal., Volume 196 (2002), pp. 162-179

[2] Ikeda, I.; Watanabe, S. Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981

[3] Malliavin, P. The Canonical diffusion above the diffeomorphism group of the circle, C. R. Acad. Sci. Paris, Ser. I, Volume 329 (1999), pp. 325-329

[4] Revuz, D.; Yor, M. Continuous Martingales and Brownian Motion, Grundlehren Math. Wiss., 293, Springer-Verlag, 1991

[5] Stroock, D.W.; Varadhan, S.R.S. Multidimensional Diffusion Processes, Springer-Verlag, 1979

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