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Diffusion Processes on Solvable Groups of Upper Triangular 3x3 matrices. Applications in Asian and Basket Options.
Title
Diffusion Processes on Solvable Groups of Upper Triangular 3x3 matrices. Applications in Asian and Basket Options.
Author
Simonsen, Julia
Date Created
2020
Subjects--Topical
Mathematics
Description
One of the questions in algebraic groups is about the asymptotic behavior of the probability of return of a random walk, which closely related on the growth rate of a group. Upper-triangular matrices form a group. Solvable groups have an exponenti...
ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS
Title
ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS
Author
Hulko, Artem
Date Created
2018
Subjects--Topical
Mathematics
Description
In this dissertation we find estimates for the total number of eigenvalues of non-self-adjoint operators. We consider five different operators, three of them discrete and two continuous. Discrete operators are as follows: Schrödinger operator defi...
Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations
Title
Limit Cycles in Two Dimensional Systems of Ordinary Differential Equations
Author
Rowe, Ashley
Date Created
2018
Subjects--Topical
Mathematics
Description
This thesis concerns cycles, i.e., topological ovals, in the phase portraits of systems of first order ordinary differential equationsin the plane, with an emphasis on limit cycles, cycles that are isolated from all other cycles. These are of fund...
On the spectral theory of 1-D Schrodinger operator with random sparse potentials
Title
On the spectral theory of 1-D Schrodinger operator with random sparse potentials
Author
Cook, Thomas
Date Created
2019
Subjects--Topical
Mathematics
Description
The goal of this dissertation is to develop a spectral theory for the Schr\"odinger operator with sparse random potential. To do this, we will first reformulate theories for sparse deterministic potentials. This includes a general development of t...