Date of Award:
5-1985
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Department name when degree awarded
Mathematics
Committee Chair(s)
Michael Brennan
Committee
Michael Brennan
Abstract
This work is a study of the relationship between Brownian motion and elementary, linear partial differential equations. In the text, I have shown that Brownian motion is a Markov process, and that Brownian motion itself, and certain Stochastic processes involving Brownian motion are also martingales. In particular, Dynkin's formula for Brownian motion was shown. Using Dynkin's formula and Brownian motion, I then constructed solutions for the classical Dirichlet problem and the heat equation, given by Δu=0 and ut= 1/2Δu+g, respectively. I have shown that the bounded solution is unique if Brownian motion will always exit the domain of the function once it has started at a point in the domain. The heat equation also has a unique bounded solution.
Checksum
c6f04f6948c9fd002cd70d51bcd5ff8f
Recommended Citation
McKay, Steven M., "Brownian Motion Applied to Partial Differential Equations" (1985). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6992.
https://digitalcommons.usu.edu/etd/6992
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