Sur la methode de Picard (EDO et EDS). (About the Picard method (EDO and EDS)). (French) Zbl 0629.60065

Feyel, Denis

Sémin. probabilités XXI, Lect. Notes Math. 1247, 515-519 (1987).

[For the entire collection see Zbl 0606.00022.]
The author of this note remarks that, when studying an ordinary or stochastic differential equation with Lipschitz coefficients, one can apply directly the fixed point theorem by choosing conveniently the Banach space; exponential growth of the solution is also given.

Reviewer: J.Picard

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

Picard’s iterative method; Lipschitz coefficients; fixed point theorem; exponential growth of the solution