Random Processes

Random Processes in Python

Animated Visualization of Random Walks in Python

Animation of a simple random walk by using the MatplotLib Animation API. Source code in file:

• random_walk_animation.ipynb: the source code for the random walk simulation and animation

Animated Visualization of Brownian Motion in Python

Illustration of the Brownian Motion construction from a simple random walk using the Donsker's Invariance Principle. Source code in file:

• brownian_motion_animation.ipynb

Random Walks Have Never Been Funnier: Drifted Brownian Motion in Python

Extending the bare Brownian Motion with volatility and drift. We illustrate these two proparties with an animated visualization using Matplotlib's Animation API. Source code:

• drifted_brownian_motion.ipynb

Forget Determinism, see Randomness in Action: How to Model Stock Price

Transforming the Drifted Brownian Motion from a process with additive increments to a process with multiplicative increments. This is well suited for modelling stock price data. We analyze and animate one interesting property of the process: for certain conditions, it has zero mean and infinite variance. Source code:

• geometric_brownian_motion.ipynb