We consider three stochastic models for fractionated irradiation of tumors. Two of them are based on the iterated birth-and-death processes with linear rates. For the first of them, the initial number of the clonogenic tumor cells is not random, and all the marginals belong to the family of Feller-Arley distributions. The second model stipulates a randomized Poisson initial condition for the number of of such cells which implies that all the marginals are from the Pólya-Aeppli family of probability laws. The third model pertains to a Poisson initial condition and discrete stable marginals which could be related to a more rapid growth of tumor. We discuss various approximations as well as such characteristics as the tumor control probability and the probability of cure. In the first part, we will provide the distribution theory background.

Bio: Vladimir Vinogradov is a Canadian-American mathematician born and educated in the former Soviet Union. Dr. Vinogradov holds a Professor - status-only appointment at the University of Toronto, Scarborough. He is a Professor of Mathematics at Ohio University in Athens, Ohio. He earned his M.Sc. in Mathematics and Ph.D. in Probability and Statistics from Moscow State University with his dissertation published in his monograph "Refined Large Deviation Limit Theorems". Professor Vinogradov has taught in various post-secondary institutions of Canada, Japan, Russia and U.S.A., and held an NSERC Canada postdoctoral fellowship at Carleton University. His research focuses on various topics of Probability Theory, Stochastic Processes, Mathematical Statistics, Analysis and Financial Mathematics. Professor Vinogradov has published articles in many professional journals and presents frequently at national and international conferences. He has been recipient of a British Columbia – Asia Pacific Scholars' Award, and served on the Ontario Graduate Scholarships Committee as well as NSERC Canada external reviewer and graduate coordinator at the University of Northern British Columbia. Professor Vinogradov is advisor to Actuarial Science and Mathematical Statistics majors.