Syllabus
Rutgers University
College of Engineering
Department of Industrial Engineering
540:616 Advanced Stochastic Modeling
Instructor: Dr. M. B. Gürsoy
Office: CoRE 218
Phone: X-5465
Email: gursoy@soe.rutgers.edu
COURSE OUTLINE
 
    • Introduction and review of basic stochastic processes, CTMCs, queues
    • Renewal theory, Wald’s equation, alternating and delayed renewal process
    • Renewal reward process, regenerative process, applications in queueing and reliability
    • Markov decision processes, applications in congestion control, asset pricing
    • Martingales, stopping times
    • Optional Sampling Theorem and its Applications
    • Midterm exam
    • Random walks, exchangeable random variables
    • Applications to G/G/1 queue and ruin problem
    • Brownian motion, hitting times
    • Reflected Brownian motion, geometric, integrated Brownian motion
    • Brownian motion with drift, diffusion equations, semi-Markov processes
    • Applications

Text:

A First Course in Stochastic Processes”, by S. Karlin and H. M. Taylor, 2nd Ed., Academic Press, 1975.

References:

A First Course in Stochastic Models”, by H. C. Tijms, , Wiley, 2003.

Stochastic Processes”, by Sheldon Ross, 2nd Ed., Wiley, 1996.