for some choice of b n ↑ ∞ as n → ∞. Similar large deviation principles (LDPs) have been obtained in Denisov, Dieker and Shneer (2008) under the more general assumption of the random variables being sub-exponential. Moving forward from random variables, the notion of regular variation of càdlàg processes has been characterized in . It was aptly noted in that large deviations for such processes with heavy-tailed margins are very closely related to the notion of regular variation.A precise large deviation result for partial sum processes on the space D[0, 1] of càdlàg functions was provided in , Theorem 2.1); in fact this result was obtained for d-dimensional processes. In particular for d = 1, the authors establish that if S n = (S nt ) t∈ [0,1]
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