Article Source

• Martingale Theory

Martingale Theory

• Martingale theory I: https://youtu.be/zYjiBSe3c8g
• Martingale theory II: https://youtu.be/DGJKsBeoncI
• Martingale theory III: https://youtu.be/3si-iiciCNg
• Martingale theory IV: https://youtu.be/Z-m20CO5mhk

Abstract

We review basic facts from martingale theory. We start with discretetime parameter martingales and proceed to explain what modifications are needed in order to extend the results from discrete-time to continuous-time. The Doob-Meyer decomposition theorem for continuous semimartingales is stated but the proof is omitted. At the end of the chapter we discuss the quadratic variation process of a local martingale, a key concept in martingale theory based stochastic analysis.

Martingale Theory I

Martingale Theory II

Martingale Theory III

Martingale Theory IV