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Advanced Stochastic Processes >> Content Detail



Lecture Notes



Lecture Notes

LEC #TOPICS
1Probability Basics: Probability Space, σ-algebras, Probability Measure (PDF)
2Random Variables and Measurable Functions; Strong Law of Large Numbers (SLLN) (PDF)
3Large Deviations for i.i.d. Random Variables (PDF)
4Large Deviations Theory (cont.) (Part 1) (PDF)

Properties of the Distribution Function G (Part 2) (PDF)
5Brownian Motion; Introduction (PDF)
6The Reflection Principle; The Distribution of the Maximum; Brownian Motion with Drift (PDF)
7Quadratic Variation Property of Brownian Motion (PDF)
8Modes of Convergence and Convergence Theorems (PDF)
9Conditional Expectations, Filtration and Martingales (PDF)
10Martingales and Stopping Times (PDF)
11Martingales and Stopping Times (cont.); Applications (PDF)
12Introduction to Ito Calculus (PDF)
13Ito Integral; Properties (PDF)
14Ito Process; Ito Formula (PDF)
15Martingale Property of Ito Integral and Girsanov Theorem (PDF)
16Applications of Ito Calculus to Finance (PDF)
17Equivalent Martingale Measures (PDF)
18Probability on Metric Spaces (PDF)
19σ-fields on Measure Spaces and Weak Convergence (PDF)
20Functional Strong Law of Large Numbers and Functional Central Limit Theorem (PDF)
21G/G/1 Queueing Systems and Reflected Brownian Motion (RBM) (PDF)
22Fluid Model of a G/G/1 Queueing System (PDF)
23Fluid Model of a G/G/1 Queueing System (cont.) (PDF)
24G/G/1 in Heavy-traffic; Introduction to Queueing Networks (PDF)
25Final Notes and Ongoing Research Questions and Resources (PDF)

 








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