This course covers basic ideas and methods in applied probability and stochastic modeling. Topics include limit theory, sample path analysis, martingale methods, stochastic stability, the single server queue, renewal theory and regenerative processes. The intended audience is masters and doctoral students in programs such as EE, CS, IEOR, Statistics, Mathematics, and those in the DRO division in the Business School. (Students from all other areas are of course welcome as well.)
In terms of prerequisites, basic familiarity with probability theory and stochastic processes will be assumed (an ideal preliminary course is IEOR 6711: Stochastic Modeling I, but a more basic substitute will do as well).
The topics and material covered in this course complement those covered in IEOR 6712: Stochastic Modeling II, hence the two courses can be taken simultaneously. The exposition will be (mostly) rigorous, yet intentionally skirting some measure-theoretic details; for those interested in such details they can be found in measure theoretic textbooks and other courses. A common thread that runs through most of the course is its focus on asymptotic methods. The latter constitutes a powerful tool for the study of complex models of stochastic processing systems.