Stochastic integral in case of infinite expectation of the first exit time

A method of analysis of a multi-dimensional semi-Markov process of diffusion type in case of infinite expectation of the first exit time from a small neighborhood of the initial point is worked out. A generalization of a formula of Dynkin for this case is proved. The formula of Ito for the stochastic integral by the multi-dimensional semi-Markov process of diffusion type is derived.