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.
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.
Accepted:
Published online:
Shizan Fang 1; Tusheng Zhang 2
@article{CRMATH_2003__337_11_737_0, author = {Shizan Fang and Tusheng Zhang}, title = {A class of stochastic differential equations with {non-Lipschitzian} coefficients: pathwise uniqueness and no explosion}, journal = {Comptes Rendus. Math\'ematique}, pages = {737--740}, publisher = {Elsevier}, volume = {337}, number = {11}, year = {2003}, doi = {10.1016/j.crma.2003.10.008}, language = {en}, }
TY - JOUR AU - Shizan Fang AU - Tusheng Zhang TI - A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion JO - Comptes Rendus. Mathématique PY - 2003 SP - 737 EP - 740 VL - 337 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2003.10.008 LA - en ID - CRMATH_2003__337_11_737_0 ER -
%0 Journal Article %A Shizan Fang %A Tusheng Zhang %T A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion %J Comptes Rendus. Mathématique %D 2003 %P 737-740 %V 337 %N 11 %I Elsevier %R 10.1016/j.crma.2003.10.008 %G en %F CRMATH_2003__337_11_737_0
Shizan Fang; Tusheng Zhang. A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion. Comptes Rendus. Mathématique, Volume 337 (2003) no. 11, pp. 737-740. doi : 10.1016/j.crma.2003.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.008/
[1] Canonical Brownian motion on the diffeomorphism group of the circle, J. Funct. Anal., Volume 196 (2002), pp. 162-179
[2] Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981
[3] The Canonical diffusion above the diffeomorphism group of the circle, C. R. Acad. Sci. Paris, Ser. I, Volume 329 (1999), pp. 325-329
[4] Continuous Martingales and Brownian Motion, Grundlehren Math. Wiss., 293, Springer-Verlag, 1991
[5] Multidimensional Diffusion Processes, Springer-Verlag, 1979
Cited by Sources:
Comments - Policy