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ACKNOWLEDGEMENTS There have been many individuals in my life without whom the completion of this work would not have been possible. It is my intension to briefly recognize their contribution to my personal and professional life. I would like to thank my advisor, Dr. Christian Houdré, for his support and orientation through all my studies at Georgia Tech. In(More)
The first part of this study characterizes several properties of a reversible Markov jump process X ≡ {X t : t ≥ 0} on a general measurable space (E, E) with transition rate kernel q(x, A). The process (or the kernel q) is reversible reversible with respect to π, if π is a measure on IE such that π(dx)q(x dy) = π(dy)q(y dx). Reversibility was introduced by(More)
Boekbesprekingen mathematics, as evidenced by the number of symposia and Sym-plectic Geometry Seminars in mathematics departments around the world. Integrable Hamiltonian systems were amongst the first to be analyzed in the 19th century, a prime example being the two-body problem. However, with the discovery that the KdV equation is an integrable(More)
Dedication I would like to dedicate the dissertation to my father, Germán Riaño Cano, who was always an inspirational figure for me. iii Acknowledgements I want to thank my wife, Sandra López Bautista who has given me her unconditional support throughout these years. This dissertation is also her work. Also my children, Juan Diego and Alejandra Riaño López(More)