Une condition ctexistence et d'unicitépour les solutions fortes d'équations différentielles stochastiques
- 1 January 1980
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 4 (1) , 23-38
- https://doi.org/10.1080/17442508008833155
Abstract
We consider the following stochastic differentic equation where Z is a given semimartingale and K is a given process with right-continuous and lefthand limited paths, on some filtered probability space . We prove the exixtence of a strong solution (or: solution-process) on this space, under an at most linear growth condition on g, when the usual Lipschitz Countinuity of g,(ω,x) in x is replaced by weaker hypothese, namely that g s (ω,x) is continuous in x and satisfies a monotonicity condition related to the process Z.Keywords
This publication has 7 references indexed in Scilit:
- Integrales stochastiques par rapport a une semimartingale vectorielle et changements de filtrationPublished by Springer Nature ,1980
- On the Existence, Uniqueness, Convergence and Explosions of Solutions of Systems of Stochastic Integral EquationsThe Annals of Probability, 1977
- Equations differentielles stochastiquesPublished by Springer Nature ,1977
- Sur une équation d'évolution stochastiqueBulletin de la Société Mathématiques de France, 1976
- On the existence and unicity of solutions of stochastic integral equationsProbability Theory and Related Fields, 1976
- Introduction et notations generalesPublished by Springer Nature ,1976
- Equations aux derivees partielles stochastiques non lineairesIsrael Journal of Mathematics, 1972