c©Dynamic Publishers, Inc. PREVENTION OF EXPLOSIONS IN SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS BY NOISE PERTURBATION

ABSTRACT. The existence and uniqueness of global solutions of a class of scalar stochastic functional differential equations of Ito ̂ type is studied. It is not assumed, however, that the coefficients need to satisfy global linear bounds. For a subclass of these equations, it is known that the associated deterministic equation, which is not noise-perturbed, explodes in finite time. Therefore, a noise term may be added in such a way as to prevent the deterministic explosion. Finite dimensional analogues are also treated. AMS (MOS) Subject Classification. 34K50, 34K15, 60H10. 1