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Published in:
2012 | OriginalPaper | Chapter
Perturbations Leading to Markov Processes
Authors : Mark I. Freidlin, Alexander D. Wentzell
Published in: Random Perturbations of Dynamical Systems
Publisher: Springer Berlin Heidelberg
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In Chap. 5 the large-deviation results of Chap. 4 are generalized to include not only diffusion processes with small variable diffusion, but also to families of locally infinitely divisible Markov processes with small randomness. The action functional in these cases is expressed as the integral involving the test function and its first derivative, using the Legendre transformation of some characteristic of the Markov process in question. Some part of the proofs is based on a generalization of H. Cramér’s transformation the he applied to large deviations for sums of independent random variables.