Stringy Hodge numbers of threefolds

Batyrev has defined the stringy E-function for complex varieties with at most log terminal singularities. It is a rational function in two variables if the singularities are Gorenstein. Furthermore, if the variety is projective and its stringy E-function is a polynomial, Batyrev defined its stringy Hodge numbers essentially as the coefficients of this E-function, generalizing the usual notion of Hodge numbers of a nonsingular projective variety. He conjectured that they are nonnegative. We prove this in the threefold case in full generality, and also for fourfolds and fivefolds with at most isolated Gorenstein terminal singularities. In addition, we give an explicit description of the stringy Hodge numbers in these cases, and we suggest a possible generalized definition of stringy Hodge numbers if the E-function is not a polynomial.