Graduate Thesis Or Dissertation
 

Large deviation principles for random measures

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  • Large deviation theory has experienced much development and interest in the last two decades. A large deviation principle is the exponential decay of the probability of increasingly rare events and the computation of a rate or entropy function which measures the rate of decay. Within the probability literature there has been much use made of these rates in diverse applications. These large deviation principles have been discovered for independent and identically distributed random variables, as well as random vectors and these have been extended to some cases of weak dependence. In this thesis we prove large deviation principles for finite dimensional distributions of scaling limits of random measures. Functional approaches to large deviation theory using test functions as dual objects to random measures are also developed. These results are applied to some important classes of models, in particular Poisson point processes, Poisson center cluster processes and doubly stochastic point processes.
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file details HwangDae-Sik.pdf 2017-08-07 Pubblico Scaricare