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Evolution Processes and the Feynman-Kac Formula by Brian Jefferies (Paperback, 2010)

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ISBN-13: 9789048146505, 978-9048146505. Evolution Processes and the Feynman-Kac Formula. This book is an outgrowth of ideas originating from 1. It is more than likely that with his input, the approach and areas of emphasis of the resulting exposition would have been quite different from what we have here.

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The evolution of a physical system can often be described in terms of a semigroup of linear operators. Observations of the system may be modelled by a spectral measure. A combination of these basic objects produces a family of operator valued set functions, by which perturbations of the evolution are represented as path integrals. In this book, random processes measured by operator valued set functions - evolution processes - are systematically examined for the first time. The Feynman-Kac formula, representing perturbations of the heat semigroup in terms of integrals with respect to Wiener measure, is extended in a number of directions: to other countably additive processes, not necessarily associated with a probability measure; to unbounded processes such as those associated with Feynman integrals; and to random evolutions. Audience: Researchers in mathematical physics, functional analysis and stochastic processes.