This project is about the application of random walks and aims to investigate the relationship between the stochastic process and heat equation. This shall be achieved by examining the theoretical analysis and simulating numerical computations. Lawler’s book Random Walk and the Heat Equation will be the main study resource. This project will involve investigating the heat equation from a probabilistic perspective and the interplay between deterministic and stochastic, discrete, and continuous processes. Furthermore, it will address additional information that can be obtained by considering micro level movements of individual random particles. The simulations of random walk and traditional heat equation will be conducted to support the theoretical analysis and findings.
Huan Chen is a student at Monash University. Though his degree is engineering, he is working hard to reach further maths study. He is interested in stochastic processes and probability, particularly in random walks and financial mathematics. He prefers to work with pen and paper as it brings inspiration although his handwriting is poor.