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Ron McKay and Song Du's Project SummaryOur project invovlved one-dimensional random walk and two-dimensional Brownian motion simulation. Specifically, we were looking at first passage times of these simulations.In the one-dimensional random walk case, the question arises, "What is the probability of taking an n-step walk without reaching a distance, lambda, from the origin?" This question can be rephrased as, "What is the probability that the time lambda is reached is greater than n?" This probability has been theoretically shown to be P{T>n} ~ cn-alpha where T is the time that lambda is reached. Using Matlab to run a large number of simulations, we determined the value of the exponent alpha. For the two-dimensional Brownian motion case, we looked at the probability that a particle in Brownian motion stayed within a bounded region for a particular amount of time. We then scaled the bounded region and compared the probability that the particle remained in the region to the scaling value. |
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VIGRE Steering Committee Department of Mathematics University of Utah 155 South 1400 East; Room 233 Salt Lake City, UT 84112 email: viscom@math.utah.edu |
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