Subscribe to DSC Newsletter

A Simple Introduction to Complex Stochastic Processes - Part 2

In my first article on this topic (see here) I introduced some of the complex stochastic processes used by Wall Street data scientists, using a simple approach that can be understood by people with no statistics background other than a first course such as stats 101. I defined and illustrated the continuous Brownian motion (the mother of all these stochastic processes) using approximations by discrete random walks, simply re-scaling the X-axis and the Y-axis appropriately, and making time increments (the X-axis) smaller and smaller, so that the limiting process is a time-continuous one. This was done without using any complicated mathematics such as measure theory or filtrations.

Here I am going one step further, introducing the integral and derivative of such processes, using rudimentary mathematics. All the articles that I've found on this subject are full of complicated equations and formulas. It is not the case here. Not only do I explain this material in simple English, but I also provide pictures to show how an Integrated Brownian motion looks like (I could not find such illustrations in the literature), how to compute its variance, and focus on applications, especially to number theory, Fintech and cryptography problems. Along the way, I discuss moving averages in a theoretical but basic framework (again with pictures), discussing what the optimal window should be for these (time-continuous or discrete) time series.

You can read the full article, here

Upcoming DSC Webinars

DSC Resources

Views: 65

Comment

You need to be a member of AnalyticBridge to add comments!

Join AnalyticBridge

Follow Us

On Data Science Central

On DataViz

On Hadoop

© 2018   AnalyticBridge.com is a subsidiary and dedicated channel of Data Science Central LLC   Powered by

Badges  |  Report an Issue  |  Privacy Policy  |  Terms of Service