Genericity in Deterministic and Stochastic Differential Equations
Résumé
We prove that the convergence of the approximation with time delay, as well as pathwise uniqueness, are generic properties in ordinary differential equations as well as in stochastic differential equations. This is done in the case where the coefficients are neither bounded nor time continuous. The approximation with time delay is used to obtain existence of weak solutions for SDE. We also prove L^2-convergence of this approximation when only pathwise uniqueness is assumed.