Lecture 14: Stochastic Processes II

MIT 18.642 Topics in Mathematics with Applications in Finance, Fall 2024
Instructor: Peter Kempthorne
View the complete course: https://ocw.mit.edu/courses/18-642-to...
YouTube Playlist:    • MIT 18.642 Topics in Mathematics with Appl...  

Brownian motion is a fundamental stochastic process characterized by continuous, random, and independent increments with normally distributed changes over time, whose variance grows proportionally with the time interval. It serves as a mathematical model for diverse natural and financial phenomena, exhibiting key properties such as the Markov property, reflection principle, quadratic variation, and extensions like Brownian motion with drift, reflected and absorbed Brownian motions, and the Brownian bridge, all crucial for understanding random dynamics and derivative pricing.

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ

We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.