In this project we want to visualize and study small time behavior of several strongly degenerate diffusion processes. First we start with a Kolmogorov process and its lift to a diffusion process in the first Heisenberg group. Then we move on to diffusions that can be lifted to the Engel group. If time allows, we will also look at a diffusion that has a solvable structure, which is of great interest in finance.
Completion of Calculus 3. Good programing skill.