A Data Science Central Community

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**

- Data Contributions to a Conversational AI Platform - March 28
- rEvolutionize Your Analytics: Break Barriers to Insight - March 27
- The Analytics Revolution: Evolution or Extinction - March 20

**DSC Resources**

- Subscribe to our Newsletter
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- Hire a Data Scientist | Search DSC | Classifieds | Find a Job
- Post a Blog | Forum Questions

© 2020 AnalyticBridge.com is a subsidiary and dedicated channel of Data Science Central LLC Powered by

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

**Most Popular Content on DSC**

To not miss this type of content in the future, subscribe to our newsletter.

- Book: Statistics -- New Foundations, Toolbox, and Machine Learning Recipes
- Book: Classification and Regression In a Weekend - With Python
- Book: Applied Stochastic Processes
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- How to Automatically Determine the Number of Clusters in your Data
- New Machine Learning Cheat Sheet | Old one
- Confidence Intervals Without Pain - With Resampling
- Advanced Machine Learning with Basic Excel
- New Perspectives on Statistical Distributions and Deep Learning
- Fascinating New Results in the Theory of Randomness
- Fast Combinatorial Feature Selection

**Other popular resources**

- Comprehensive Repository of Data Science and ML Resources
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- 100 Data Science Interview Questions and Answers
- Cheat Sheets | Curated Articles | Search | Jobs | Courses
- Post a Blog | Forum Questions | Books | Salaries | News

**Archives:** 2008-2014 |
2015-2016 |
2017-2019 |
Book 1 |
Book 2 |
More

**Most popular articles**

- Free Book and Resources for DSC Members
- New Perspectives on Statistical Distributions and Deep Learning
- Time series, Growth Modeling and Data Science Wizardy
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- How to Automatically Determine the Number of Clusters in your Data
- Fascinating New Results in the Theory of Randomness
- Hire a Data Scientist | Search DSC | Find a Job
- Post a Blog | Forum Questions

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

Join AnalyticBridge