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Transference and Szego's theorem for measure preserving representations
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] We prove analogues of the classical Szeg̈o's theorem concerning approximation by polynomials on the unit circle, and Jensen's inequality involving the ...
A class of Gorenstein Artin algebras of embedding dimension four
(University of Missouri--Columbia, 2007)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let R be a polynomial ring in n variables and I be a homogeneous ideal in R. Such an ideal I is called Gorenstein if the quotient R/I has a free ...
Volatility estimation and price prediction using a hidden Markov model with empirical study
(University of Missouri--Columbia, 2007)
This work provides a solid development of a hidden Markov model (HMM) from the economic insight to the mathematic formulation. In this model, we assume both drift and volatility of the security return process are driven ...
Trace formulae in finite von Neumann algebras
(University of Missouri--Columbia, 2007)
The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for ...