APTS Applied Stochastic Processes
Preliminary Material
1
Introduction
1.1
Learning outcomes
2
Expectation and probability
2.1
Probability
2.2
Conditional probability
2.3
Expectation
2.4
Independence
2.5
Generating functions
2.6
Uses of generating functions
2.7
Conditional Expectation (I): property-based definition
2.8
Conditional Expectation (II): some other properties
2.9
Conditional Expectation (III): Jensen’s inequality
2.10
Limits versus expectations
3
Markov chains
3.1
Basic properties for discrete time and space case
3.2
Example: Models for language following Markov
3.3
(Counter)example: Markov’s other chain
3.4
Irreducibility and aperiodicity
3.5
Example: Markov tennis
3.6
Transience and recurrence
3.7
Recurrence/transience for random walks on
\(\mathbb Z\)
3.8
Equilibrium of Markov chains
3.9
Sums of limits and limits of sums
3.10
Continuous-time countable state-space Markov chains (a rough guide)
3.11
Example: the Poisson process
3.12
Example: the M/M/1 queue
4
Some useful texts
4.1
Free on the web
4.2
Going deeper
References
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APTS Applied Stochastic Processes
References