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Statistics
Stochastic Processes
1. Foundations of Probability Theory
2. Introduction to Stochastic Processes
3. Discrete-Time Markov Chains
4. Poisson Processes
5. Continuous-Time Markov Chains
6. Renewal Theory
7. Martingales
8. Brownian Motion
9. Stochastic Calculus
10. Stationary Processes
11. Applications in Queueing Theory
12. Applications in Finance
13. Applications in Biology and Population Dynamics
14. Applications in Physics and Engineering
13.
Applications in Biology and Population Dynamics
13.1.
Branching Processes
13.1.1.
Galton-Watson Process
13.1.2.
Extinction Probabilities
13.1.3.
Critical Branching
13.1.4.
Continuous-Time Branching
13.2.
Epidemic Models
13.2.1.
SIR Model
13.2.1.1.
Deterministic Version
13.2.1.2.
Stochastic Version
13.2.2.
SIS Model
13.2.3.
SEIR Model
13.2.4.
Threshold Theorems
13.3.
Population Growth Models
13.3.1.
Birth-Death Models
13.3.2.
Logistic Growth
13.3.3.
Competition Models
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14. Applications in Physics and Engineering