Chapter 0: General

0.1  Esma6789.pdf

0.2  Syllabus

0.3  Homeworks and Exams

Chapter 1: Probability

1.1  Basics of Probability Theory

1.2  Random Variables and Random Vectors

1.3  Expectation of R.V.’s

1.4  Some Standard Random Variables

1.5  Functions of a R.V. - Transformations

1.6  Inequalities and Limit Theorems

1.7  Stochastic Processes - General Comments

1.8  Measure Theory

Chapter 2: Poisson Process and Renewal Theory

2.1  Poisson Process

2.2  Generalizations of Poisson Process

2.3  Renewal Theory

Chapter3: Markov Chains and Markov Processes

3.1  Discrete - time Markov Chains

3.2  Examples of Discrete - time Markov Chains

3.3  Continuous-time Markov Chains

Chapter 4: Other Stochastic Processes

4.1  Martingales

4.2  Brownian Motion

4.3  Stochastic Differential Equations

4.4  Stationary Processes and Ergodic Theory

4.5  Queuing Systems

Chapter 5: Statistical Analysis of Stochastic Processes

5.1  Statistics

Chapter 6: Simulating Stochastic Processes

6.1  Introduction to R

6.2  Useful R commands

6.3  Standard Methods

6.4  MCMC Methods