Introduction to Stochastic Processes

Lecture Notes

SES #	TOPICS
1	Introduction to Finite Markov Chains (PDF)
2	Markov Chains: Stationary Distribution (PDF)
3	Markov Chains: Time-reversal (PDF)
4	Introduction to Markov Chain Mixing (PDF)
5	Stationary Times (PDF)
6	Lower Bounds on Mixing Times (PDF)
7	Summary on Mixing Times (PDF)
8	Random Walk on Networks 1 (PDF)
9	Random Walk on Networks 2 (PDF)
10	Hitting Times (PDF)
11	Summary on Random Walk on Networks (PDF)
12	Countable State Space Chain 1 (PDF)
13	Countable State Space Chain 2 (PDF)
14	Midterm Exam (No Lecture Notes)
15	Conditional Expectation and Introduction to Martingales (PDF)
16	Martingales: Optional Stopping Theorem (PDF)
17	Martingales: Convergence (PDF) Almost Sure Convergence (PDF)
18	Martingales: Uniformly Integrable (PDF)
19	Galton-Watson Tree (PDF)
20	Poisson Process (PDF)
21	Continuous Time Markov Chain (PDF)
22	Infinitesimal Generator (PDF)
23	Irreducible and Recurrence (PDF)
24	Stationary Distribution (PDF)