DNA methylation is essential for the normal development and functioning of organisms. This volume discusses the latest developments in this very active field of research. It presents the evolution of DNA methylation, mammalian DNA methyltransferases, DNA methylation and demethlyation, DNA methylation and silencing and the role it plays in medicine including cancer.

* Discusses new discoveries, approaches, and ideas * Contributions from leading scholars and industry experts * Reference guide for researchers involved in molecular biology and related fields

Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability.

This advanced text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Geared toward graduate students, "Markov Processes and Potential Theory" assumes a familiarity with general measure theory, while offering a nearly self-contained treatment.
Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual processes and potential theory. Exercises appear throughout the text, and a selection of notes and comments features historical references and credits. Robert M. Blumenthal is Professor Emeritus of Mathematics at the University of Washington, and Ronald K. Getoor is Professor Emeritus of Mathematics at the University of California at San Diego.