In this paper we prove a comparison theorem for the stochastic di¤erential equation dX(t) = (A(t)X(t) + F (t;X(t))) dt+M (t;X(t)) dW (t) + R L2 M (t;X(t))x ~ N(dt; dx), t 2 [ 0; T ], driven by a Wiener noise W and a Poisson noise ~ N . The di¤usion coe¢ cients M and M are given by multiplication operators. The equation is considered in Lpspaces with a …nite weight measure over a (possibly unbou...

Azriel Levy (1934–) did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcin...

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We present a novel noisy channel model for correcting text produced by English as a second language (ESL) authors. We model the English word choices made by ESL authors as a random walk across an undirected bipartite dictionary graph composed of edges between English words and associated words in an author’s native language. We present two such models, using cascades of weighted finitestate tra...

Title of dissertation: DEPENDENCE STRUCTURE IN LEVY PROCESSES AND ITS APPLICATION IN FINANCE Qiwen Chen, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dilip B. Madan Department of Finance In this paper, we introduce DSPMD, discretely sampled process with prespecified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified mar...

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable c...

OBJECTIVE To examine the effect of the application, and removal, in the Northern Territory of a levy on the sale of cask wine--a beverage shown to contribute disproportionately to alcohol-related harm. METHOD Using data on licensee purchases of alcoholic beverages and ABS population data, estimates were made of per capita consumption of pure alcohol by beverage type. Time series variables wer...

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm u...