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Stochastic Processes, and Development of the Barndorff-Nielsen and Shephard Model for Financial Markets
(North Dakota State University, 2022)
In this paper, we introduce Brownian motion, and some of its drawbacks in connection to the financial modeling. We then introduce geometric Brownian motion as the basis for European call option pricing as we navigate our ...
Enumeration of Reduced Words of Length N for Coxeter Groups via BrinkHowlett Automaton
(North Dakota State University, 2022)
The overall goal of this paper is to give a method of computing out how many words of length n there are for any Coxeter group via its Brink-Howlett automaton. [6] [7] To build our automaton, we focus on Coxeter systems ...
New Perspectives on Promotion and Rowmotion: Generalizations and Translations
(North Dakota State University, 2022)
We define P-strict labelings for a finite poset P as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on B-bounded Q-partitions of ...