Abstract: In order to predict how coastlines will evolve over time, it is very important to be able to accurately model the heights of waves as they approach the shore and undergo both shoaling and breaking. Ocean waves are random, with energy distributed across the different frequencies according to spectra such as the JONSWAP spectrum; thus, it is important to consider the probability distribution for the heights of shoaling waves. In this talk, I will give an overview of the topic of stochastic differential equations, followed by a demonstration of the basic techniques used to reformulate the amplitudes of the wave envelopes in this manner.