Picard, Jean Transformations and anticipative equations for Poisson processes. (Transformations et équations anticipantes pour les processus de Poisson.) (French) Zbl 0856.60059 Ann. Math. Blaise Pascal 3, No. 1, 111-123 (1996). Summary: We prove the existence and uniqueness of a solution for stochastic anticipative equations driven by a point Poisson process. For a particular class of linear equations, the solution may be interpreted as the Radon-Nikodým density of an anticipative transformation of the Poisson process. Cited in 2 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:existence and uniqueness of a solution for stochastic anticipative equations; Radon-Nikodým density; anticipative transformation of the Poisson process PDF BibTeX XML Cite \textit{J. Picard}, Ann. Math. Blaise Pascal 3, No. 1, 111--123 (1996; Zbl 0856.60059) Full Text: DOI Numdam EuDML References: [1] R. Buckdahn , Anticipative Girsanov transformations and Skorohod stochastic differential equations , Memoirs Amer. Math. Soc. 111 ( 1994 ), Number 533 . MR 1219706 | Zbl 0849.60053 · Zbl 0849.60053 [2] D. Feyel , Sur la méthode de Picard (EDO et EDS) , dans, Séminaire de Probabilités XXI , Lect. N. Math. 1247 Springer , 1987 . Numdam | MR 942001 | Zbl 0629.60065 · Zbl 0629.60065 · numdam:SPS_1987__21__515_0 · eudml:113611 [3] J.A. León , J. Ruiz de Chávez et C. Tudor , Anticipating semilinear stochastic equations on the Poisson space , à paraître. · Zbl 0860.60035 [4] D. Nualart , The Malliavin calculus and related topics , Probab. and Applic. , Springer , 1995 . MR 1344217 | Zbl 0837.60050 · Zbl 0837.60050 [5] D. Ocone et E. Pardoux , A generalized Ito-Ventzell formula, Application to a class of anticipating stochastic differential equations , Ann. Institut H. Poincaré, Probab. Stat. 25 ( 1989 ), 1 39 - 72 . Numdam | MR 995291 | Zbl 0674.60057 · Zbl 0674.60057 · numdam:AIHPB_1989__25_1_39_0 · eudml:77339 [6] J. Picard , Formules de dualité sur l’espace de Poisson , Ann. Institut H. Poincaré, Probab. Stat. , à paraître. Numdam | MR 1411270 | Zbl 0859.60045 · Zbl 0859.60045 · numdam:AIHPB_1996__32_4_509_0 · eudml:77544 [7] N. Privault , Linear Skorohod stochastic differential equations on Poisson space , à paraître. · Zbl 0847.60046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.