Iterated logarithm law for anticipating stochastic differential equations (Q939124)

Anticipating stochastic differential equations (SDEs) is an interesting extension of the theory of SDEs, with a number of potential applications. The relative stochastic calculus as well as question of existence and uniqueness have been settled, however, there still remain open questions concerning for instance asymptotic results. In this work, a functional law of iterated logarithm is proved for an anticipating ordinary stochastic differential equation, of the Stratonovich type, driven by Wiener processes. The result is an interesting generalization of Strassen theorem for stochastic processes generated by anticipating SDEs. The proof of the result relies on the large deviations principle for anticipating SDEs as stated by Millet, Nualart and Sanz-Sole, which allows the characterization of the long time dynamics of the anticipating SDE in terms of the solution of a deterministic ordinary differential equations and a variational problem.