Contents:
Brownian motion, General state space Markov chains, Weak convergence, Continuous-time Martingales, Ito calculus, Stochastic geometry Introduction to Stationary Poisson Point process, Poisson Voronoi cells and its properties. Advanced queueing topics - Fluid limits, Diffusion approximation, Mean-field analysis, etc.
References:
[1] Oksendal, Bernt. "Stochastic di013erential equations." Stochastic di013erential equations. Springer Berlin Heidelberg, 2003.
[2] Ioannis Karatzas, and Steven Shreve. "Brownian motion and stochastic calculus." Vol. 113. Springer Science & Business Media, [3] Bilhngsley, Patrick. "Convergence of probability measures." , Wiley Series in Probability and Mathematical Statistics", New York, 1968.
[4] Sean Meyn and Richard L. Tweedie, "Markov Chains and Stochastic Stability", Springer-Verlag London Ltd, 1993.
[5] P. Billingsley, "Probability and Measure", third ed., Wiley- Interscience, New York, 1995.
[6] Sean Meyn "Control techniques for complex networks", Cambridge University Press, 2008.
[7] F. Baccelli and B. Baszczyszyn, "Stochastic Geometry and Wireless Networks" Volume I, NowPublishers, 2010.