Large deviations for a class of anticipating stochastic differential equations (Q1203661)

The authors consider the family of stochastic differential equations on \(R^ d\), \[ X_ t^ \varepsilon=X^ \varepsilon_ 0+\sqrt\varepsilon\int^ t_ 0\sigma(X_ s^ \varepsilon) \circ dW_ s+\int^ t_ 0b(X^ \varepsilon_ s)ds, \] where \(\varepsilon>0\), \(\{X^ \varepsilon_ 0\}\) is a family of \(d\)-dimensional random vectors which may depend on the whole path of \(W_ t\) and the stochastic integral is a generalized Stratonovich integral; \(W_ t\) is a standard \(k\)-dimensional Wiener process. The large deviations estimates for the laws of \(\{X^ \varepsilon_ \bullet\}\), under some hypotheses on the family of initial conditions, are proved.