Abstract
The finite dimensional LDPs considered in Chapter 2 allow computations of the tail behavior of rare events associated with various sorts of empirical means. In many problems, the interest is actually in rare events that depend on a collection of random variables, or, more generally, on a random process. Whereas some of these questions may be cast in terms of empirical measures, this is not always the most fruitful approach. Interest often lies in the probability that a path of a random process hits a particular set. Questions of this nature are addressed in this chapter. In Section 5.1, the case of a random walk, the simplest example of all, is analyzed. The Brownian motion counterpart is then an easy application of exponential equivalence, and the diffusion case follows by suitable approximate contractions. The range of applications presented in this chapter is also representative: stochastic dynamical systems (Sections 5.4, 5.7, and 5.8), DNA matching problems and statistical change point questions (Section 5.5).
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© 2009 Springer-Verlag Berlin Heidelberg
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Dembo, A., Zeitouni, O. (2009). Sample Path Large Deviations. In: Large Deviations Techniques and Applications. Stochastic Modelling and Applied Probability, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03311-7_5
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DOI: https://doi.org/10.1007/978-3-642-03311-7_5
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-03311-7
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