Probability Theory
Measure-theoretic probability from the ground up: σ-algebras, probability spaces, filtrations, conditional expectation, and martingale theory — the language you need before any rigorous pricing derivation.
5 modules~109 min total
Prerequisites
Real analysis (limits, continuity, Lebesgue integration)Linear algebra
Modules
01
σ-Algebras and Probability Spaces
EasyProbabilityMeasure Theoryσ-AlgebrasRandom Variables
02
Lebesgue Integration and Expectation
MediumProbabilityMeasure TheoryLebesgue IntegrationExpectation
03
Conditional Expectation and the Tower Property
HardProbabilityMeasure TheoryConditional ExpectationMartingales
04
Filtrations, Adapted Processes, and Martingales
HardProbabilityMeasure TheoryFiltrationsMartingalesStopping Times
05
Lp Spaces and Modes of Convergence
MediumProbabilityMeasure TheoryLp SpacesConvergenceUniform Integrability