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Transformations and anticipative equations for Poisson processes. (Transformations et équations anticipantes pour les processus de Poisson.) (French) Zbl 0856.60059
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.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[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
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