I just released Bessel Processes Part I, the first part of a series of notes on Bessel processes. The aim is to study Bessel and Squared Bessel proceses, and use Python 🐍 to illustrate/visualise some of their main properties.
In Part I we focus on Bessel and Squared Bessel processes with integer dimension, covering:
- Definition
- Simulation and Visualisation
- Marginal Distributions, Expectation, Variance, and Probability Density Functions
- Long time behaviour
Besides, we will make some pretty plots like this one ⬇️ which helps us to enhance the understanding of the theoretical concepts.
Bessel Process Simulation
Snippet
from aleatory.processes import BESProcess
bes = BESProcess(dim=4, T=1)
fig = bes.draw(n=100, N=200, envelope=True, colormap="pink", figsize=(12,6))In Part II, we will show that Squared Bessel processes with integer dimension satisfy an Stochastic Differential Equation (SDE). This representation will allow us define Squared Bessel processes with real dimension . Finally, in Part III we will study Bessel processes with general dimension.
Link to Bessel Processes Part I
This series is part of my project “Understanding Quantitative Finance”: a collection of notes exploring topics related on QF. The idea is to use Python 🐍to illustrate the theoretical concepts and help you to get a better understanding of each topic. This project is housed in my UQF Git Repository.