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Probability and Stochastic Processes Description

Key Elements

Code

MATH 418

Formation

M1 Mathematics

Semester

2

Credits

6

Number of Teaching Hours

36

Number of Tutoring Sessions

24

Number of Laboratory Sessions

0

This course is optional

Content

Objective

Content

This course quickly reviews basic probability theory and deals with major stochastic processes including Poisson Processes, Markov Chains and Continuous-time Markov Chains, birth and death processes. Course schedule: 1. Probability review: random variables and distributions, expected values, generating functions, conditional expectation, exponential distribution, limit theorems. 2. Conditional Expectation, properties, Jensen inequality, ... 3. Martingales: definition and properties, convergence theorem of martingales. 4. Poisson Processes: definitions of Poisson Processes, inter-arrival and waiting time, time distributions, conditional distribution of arrival times, ... 5. Markov Chains: definition, Chapman-Kolmogorov equations, classification of states, limit theorems, Gambler's ruin problem, ... 6. Continuous-time Markov Chains: definitions, birth and death processes, Kolmogorov differential equations, limiting probabilities, ...