Successive Approximation of Neutral Functional Stochastic Differential Equations in Hilbert Spaces

Boufoussi, Brahim; Hajji, Salah

Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 1, pp. 183-197.

En utilisant la méthode des approximations successives, nous allons montrer un résultat d’existence et d’unicité, sous des conditions non Lipschitziennes, pour une classe d’équations fonctionelles stochastiques de type neutre dans un espace de Hilbert.

By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients

Classification : 60H20, 34F05, 34G20
Keywords: Semigroup of bounded linear operator, Fractional powers of closed operators, Successive approximation, Mild solution, Cylindrical $Q$-Wiener process.
Mot clés : Semigroupe des operteurs lineaires bornés, Puissance fractionnaire d’un opérateur borné, Approximation succéssive, Processus de Wiener.

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