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Random walks, Brownian motion and the Poisson clumping heuristic
Author
Yap, Ai Li
Supervisor
Cheang, Gerald Hock Lye
Abstract
There are several objectives to this project. The first is to investigate the properties of random walks and Brownian motion and to express Brownian motion as a limit of random walks. Secondly, we make use of the Borel-Cantelli lemmas to obtain an asymptotic boundary (a rather crude one) on the random walk and Brownian motion. Lastly, the Poisson clumping heuristic. together with the Ornstein-Uhlenbeck process, is used to derive a more refined asymptotic boundary for the Brownian motion. It must be stressed at this point that the approach used in this work is largely of a heuristic nature. The reader should not expect to see lengthy and rigorous proofs. Instead, appropriate approximation and estimations are used to deduce the desired results.
Date Issued
2000
Call Number
QC184 Yap
Date Submitted
2000