On decomposable semi-regenerative processes and their applications

The presentation consists in three parts. In the first part the history of the Smith's regeneration idea development and generalisation is considered. The main goal of this part is to remain some results about decomposable semi-regenerative processes. The second part aims to show some applications of these processes for different stochastic models. In the third part a new application of decomposable semi-regenerative processes to investigation of k-out-of-n : F system is presented.