Martingale Convergence Theorem

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (31)

Page 2 of 4

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Martingale Convergence Theorem: Version 1

Introduces the martingale convergence theorem and demonstrates its application with examples.

Reflection Principle: Proof and Observations

Covers the reflection principle and martingale writing in simple symmetric random walks.

Martingales and Stochastic Integration

Covers martingales, stochastic integration, and localizing processes using stopping times.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Optional Stopping Theorem

Explores stopping times, the optional stopping theorem, F-measurable random variables, and martingales.

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.