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.
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