On Markov diffusion processes with delayed reflection from interval's boundary

A continuous semi-Markov process taking values in a closed interval is considered. This process coincides with a Markov diffusion process inside the interval. Thus violation of the Markov property is possible only at extreme points of the interval. A sufficient condition for a semi-Markov process to be Markov is proved. It is proved that besides of Markov processes with instantaneous reflection from boundaries of the interval there exists a class of Markov processes with delayed reflection from them. Such a process has a positive average measure of time for its trajectory to be on the boundaries. Thus the other proof of the similar result of Gihman and Skorokhod (1968) is obtained. Bibl. – 5 titles.