A stochastic differential equation (SDE) aims to relate a stochastic process to its composition of random components and base deterministic function. As the relation process is prolonged over time, solutions arise under an initial condition and boundary conditions. Therefore solutions of stochastic differential equations exist and are unique (see app.). For this simulation, the Euler–Maruyama (EM) method will be used to approximate and simulate standard Brownian particle motion.
Emma Gau (2019). Euler–Maruyama Method (https://www.mathworks.com/matlabcentral/fileexchange/69430-euler-maruyama-method), MATLAB Central File Exchange. Retrieved .