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NCRG

DISCRETE STOCHASTIC PROCESS

DISCRETE STOCHASTIC PROCESS

 

This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of discrete stochastic processes, which evolve in time via random changes occurring at discrete fixed or random intervals.

 

 

Topics include

Poisson process

Markov chain

Renewal process

Random walks

Martingales

 

 

1. Introduction and probability review

2. Laws of large numbers, convergence

3. Poisson (the perfect arrival process)

4. Poisson combining and splitting

5. Form Poisson to Markov

6. Finite-state Markov chain; the matrix approach

7. Markov rewards and dynamic programming

8. Renewals and the strong law of larghe numbers (SLLN)

9. Renewals: strong law and rewards

10. Renewal rewards, stopping trials, and Wald's equality

11. Little, M/G/1, ensemble averages

12. The last renewal

13. Renewals and countable state Markov

14. Countable-state Markov chains

15. Countable-state Markov chains and processes

16. Countable-state Markov processes

17. Markov processes and random walks

18. Hypothesis testing and radnom walks

19. Random walks and thresholds

20. Martingales (plain, sub and super) & Martingales: stopping and converging

 


Textbook : Stochastic Processes, Theory for Applications by Robert G. Gallager


 

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