Random Walk Approximation to Brownian Agents (2015)

Undergraduate: David Clancy

Faculty Advisor: Wai-Tong Fan
Department: Mathematics

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Brownian motion is a process that arises in many scientific fields. This research attempts to model one of the aspects of the continuous Brownian motion by simulating discrete random walks. More specifically, Monte Carlo methods allow the random walk simulations to approximate the time a particle spends near the boundary of a domain and compare this result to the theoretical result given by the continuous model. The theoretical results are given by solutions to partial differential equations on a square domain and by changing the way the particle interacts with the boundary gives approximations to solutions of these partial differential equations with differing initial conditions.