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Published in:
2012 | OriginalPaper | Chapter
Action Functional
Authors : Mark I. Freidlin, Alexander D. Wentzell
Published in: Random Perturbations of Dynamical Systems
Publisher: Springer Berlin Heidelberg
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In Chap. 3, the main notion of the large deviation theory, the action functional (rate function) for a family of probability measures (family of stochastic processes) is introduced and its properties are discussed in detail. The Wiener process with a small factor and its continuous transformations, in particular, Gaussian processes and diffusion processes with a constant diffusion matrix are considered as examples. General results concerning logarithmic asymptotics of the large deviation probabilities and the Laplace type asymptotics of expectations are presented in this chapter.