课程名称: Elements of Renewal Theory, with applications

授课教师：Alexander Iksanov（基辅国立大学计算机科学与控制论学院教授）

授课时间：2023年11月20日、11月22日、11月23日19：00-21：00

授课地点：腾讯会议：566-1076-5738

摘要: Renewal Theory is an area of Probability Theory which investigates structural and asymptotic properties of the standard random walkswith nonnegative steps and various functionals defined on them, for instance, renewal process, overshoot, undershoot etc. In the early days of Renewal Theory major contributions to itsdevelopments were made by Blackwell, Cox, Erd\{o}s, Feller, Pollard, Smith and some others. It is impossible to imagine the existence of many disciplines within Probability Theory such asqueuing theory, theory of random walks and perturbed random walks, theory of subordinators (L\'{e}vy processes with nondecreasing paths), theory of random regenerative structures (randompartitions, compositions, occupancy schemes in a random environment), reliability theory, the list could have beenextended, without the tools coming from Renewal Theory. Further, Renewal Theory is widely used in modeling many real-world phenomena and as such is an indispensable part of modern appliedmathematics.

授课教师简介：Alexander Iksanov，基辅国立大学计算机科学与控制论学院教授和运筹学系主任。他分别于2000年和2007年在基辅大学获得博士学位和数学学科授课资格，曾在波兰弗罗茨瓦夫学院、中国西安电子科技大学等多所大学担任客座教授。主要研究方向包括更新理论和分支随机游走，并且是这些领域的领军人物。他在Annals ofProbability, Probability Theory and Related Fields, Annals of Applied Probability, Annales de L'institut Henri Poincare, Bernoulli, Journal of Mathematical Analysis and Applications, Electronic Journal of Probability等刊物发表学术论文约100余篇，其中包括2篇专著。根据Scopus数据库，他在国际同行评审数学期刊和概率期刊上发表了75篇论文（包括合著），论文被引用次数为587次，h指数为13。根据谷歌学术，论文被引用次数为1457次，h指数为21。