The aim of this book is to summarize the obtained results of investigation of the boundary problems tied with distributions of boundary functionals for random processes and random walks with independent increments considered in the fluctuation theory and to draw attention to their connection with the risk theory. In the book special attention is paid to Levy processes with hyperexponentially distributed jumps. For them the unified prelimit and limit Pollaczeck-Khinchine formulas are established. They are used in the investigation of distributions of boundary functionals defining different characteristics of the risk and queueing processes. This monograph will be useful to the researchers working with probability theory and stochastic processes, in particular for those who deal with boundary problems for Levy processes and with their applications in risk theory, renewal theory, reliability theory, queueing theory, financial and actuarial mathematics, and in other applied areas. This book can be recommended to scientists, engineers, students, and post-graduate students of economical and mathematical specialities.

Autorentext

Gusak Dmytro Vasylyovych is a former leading researcher at Institute of mathematics of National Academy of Science of Ukraine, Doctor of Science in physics and mathematics. He specializes in boundary problems for processes with independent increments and in risk theory. He was a professor at Taras Shevchenko National University of Kyiv (1998-2012).