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Full-Text Articles in Probability
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
Master's Theses
In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …
Paper Structure Formation Simulation, Tyler R. Seekins
Paper Structure Formation Simulation, Tyler R. Seekins
Electronic Theses and Dissertations
On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …
One-Dimensional Excited Random Walk With Unboundedly Many Excitations Per Site, Omar Chakhtoun
One-Dimensional Excited Random Walk With Unboundedly Many Excitations Per Site, Omar Chakhtoun
Dissertations, Theses, and Capstone Projects
We study a discrete time excited random walk on the integers lattice requiring a tail decay estimate on the number of excitations per site and extend the existing framework, methods, and results to a wider class of excited random walks.
We give criteria for recurrence versus transience, ballisticity versus zero linear speed, completely classify limit laws in the transient regime, and establish a functional limit laws in the recurrence regime.