Limit theorems for hitting times of 1-dimensional generalized diffusions

Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting po ints tend to boundaries under an assumption which is slightly stronger than that the existence of limits gamma + 1 of the ratio of the mean and the va riance of the hitting time. Laplace transforms of limit distributions are m odifications of Bessel functions. Results are classified by the one paramet er {gamma}, each of which is the degree of corresponding Bessel function. I n case the limit distribution is degenerate to one point, by changing the n ormalization, we obtain convergence to the normal distribution. Regarding t he starting point as a time parameter, we obtain convergence in finite dime nsional distributions to self-similar processes with independent increments under slightly stronger assumption.