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By using a change of scale and space, we study a class of stochasticdifferential equations (SDEs) whose solutions are drift--perturbed and exhibitbehaviour analogous to standard Brownian motion including to the Law of theIterated Logarithm (LIL). Sufficient conditions ensuring that these processesobey the LIL are given.

Recurrent Solutions of Stochastic Differential Equations with Non-constant Diffusion Coefficients which obey the Law of the Iterated Logarithm