Year: 2017
Type: dissertation
Abstract: During the past few decades, the gauge and conditional gauge theorems for additive functionals have been developed by many authors in the general framework of Markov processes.The gauge theorem asserts that under suitable conditions on a Markov process X and an additive functional A, their corresponding gauge function is either identically infinite or bounded.If the latter happens, the pair (X, A) is said to be gaugeable.On the other hand, the conditional gauge theorem is related to the gauge theorem but is much deeper.The conditional gauge theorem asserts that under suitable conditions on X and A, the associated conditional gauge function is either identically infinite or bounded between two positive constants.If the latter happens, the pair (X, A) is said to be conditionally gaugeable and in this case, the Green functions of the Feynman-Kac transformed process of X by exp(A) and the underlying process X are comparable.So the infinitesimal generators of the Feynman-Kac transformed process and the underlying process share many potential theoretic properties.In this sense, it is important to know when the pair (X, A) is gaugeable or conditionally gaugeable.Recently, analytic characterizations of the gaugeability and conditional gaugeability for (X, A) have been studied by several authors.In the case of Brownian motion in the Euclidean space, Zhao [55] introduced a so-called shuttle operator and showed that (X, A) is condition-First of all, I would like to express my gratitude to my supervisor
Author: KURNIAWATY, Mila
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208524890