The Effect of Memory on Large Deviations of Moving Average Processes and Infinitely Divisible Processes

dc.contributor.authorGhosh, Souvik
dc.description.abstractLong range dependence is a very important phenomenon that has been observed in many real life situations. The large deviation principle is a very important probabilistic tool for dealing with rare events. The interaction between the two topics is investigated. We study the effect of the dependence structure of the process on large deviations in the perspective of the moving average process and the infinitely divisible process with exponentially light tails. The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional large, moderate and huge deviation principles. We apply the results to study the rate of growth of long strange segments and the rate of decay of ruin probabilities and the effect of memory on those. We study the functional large deviation principle for a general class of long range dependent infinitely divisible processes driven by a null recurrent Markov chain. We also apply the principle to obtain the rate of decay of the probability of ruin for these models.en_US
dc.identifier.otherbibid: 6397230
dc.subjectLarge Deviationsen_US
dc.subjectLong Range Dependenceen_US
dc.subjectMoving Averagesen_US
dc.subjectInfinitely Divisible Processesen_US
dc.subjectStochastic Processesen_US
dc.titleThe Effect of Memory on Large Deviations of Moving Average Processes and Infinitely Divisible Processesen_US
dc.typedissertation or thesisen_US


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