Izyumtseva O. Self-intersection local times for the random processes

The analogue of the property of self-similarity for renormalized self-intersection local times for the Wiener process is obtained. The existence of renormalized self-intersection local times for Ito processes is proved. The asymptotic behavior of renormalization for the self-intersection local times of diffusion processes is investigated. The existence of the expectation of the approximation for the self-intersection local times of the image of planar Wiener process . The existence of the self-intersection local times corresponding to some measure on the smooth curve for the Wiener process in space.