Evolution Processes and the Feynman-Kac Formula

Description:

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.

subjects: Linear operators,  Differential equations, parabolic,  Stochastic processes,  Multiple integrals,  Operator theory,  Functional analysis,  Mathematics,  Distribution (Probability theory),  Applications of Mathematics,  Measure and Integration,  Probability Theory and Stochastic Processes