MA 5014 Applied Stochastic Processes

Course Details

Discrete-Time Markov Models:
Discrete-Time Markov Chains, Transient Distributions, Occupancy Times, Limiting Behavior, First-Passage Times.
Poisson Processes:
Poisson Processes, Superposition of Poisson Processes, Thinning of a Poisson Process, Compound Poisson Processes.
Continuous-Time Markov Models:
Continuous-Time Markov Chains, Transient Analysis: Uniformization, Occupancy Times, Limiting Behavior, First-Passage Times.
Generalized Markov Models:
Renewal Processes, Cumulative Processes, Semi-Markov Processes.
Queueing Models:
Queueing Systems, Single-Station Queues, Birth and Death Queues.
Brownian Motion:
Standard Brownian Motion, Brownian Motion, First-Passage Times, Martingales and Semimartingales, Black Scholes Formula.

Course References:

Text Books:
1. V. G. Kulkarni, Introduction to modeling and analysis of stochastic systems, second edition, Springer, 2011.
1. S. M. Ross, Stochastic processes, second edition, Wiley, 1996.
2. S. Karlin and H. M. Taylor, A first course in stochastic processes, second edition, Academic Press, 1975.
3. S. M. Ross, Introduction to Probability Models, tenth edition, Academic Press, 2009.