Date of Award

Spring 1-1-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

First Advisor

William Kleiber

Second Advisor

Jem Corcoran

Third Advisor

Brian Zaharatos

Abstract

This thesis aims to develop the method of consecutive conditioning, which is used to directly simulate a stochastic process given an arbitrary covariance function. As a method for simulating stochastic processes, consecutive conditioning is useful in at least in three respects. While most methods require modeling of the covariance function prior to simulation, consecutive conditioning can be used with any arbitrary covariance function, thus introducing less error into the simulation than other methods. Second, consecutive conditioning allows us to perform very fast computations during simulation and can be used even by people who are not experts in modeling, unlike other methods which require substantial statistical work prior to simulation. Finally, this method can be used to simulate both stationary and nonstationary processes, which is particularly useful since the majority of real-world physical processes are nonstationary.

With the Kullback-Leibler divergence in hand, we validate the consecutive conditioning method as follows. After executing our method on a simulated distribution, we compare the resulting distribution with the true distribution for calculating the KL values. Then, we demonstrate that the consecutive conditioning works well on different covariance functions by applying it to a different series of simulations. First, we use a consecutive conditioning with several different covariance functions to simulate two time points of a stochastic process, then compare the results to determine the best covariance function for our method. Finally, we use our method to generate five time points from a stochastic process in both uninitialized and initialized cases, then evaluate the results.

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