Mogulskii, A. A. Large deviations for processes with independent increments. (English) Zbl 0769.60026 Ann. Probab. 21, No. 1, 202-215 (1993). The large deviation principle (LDP) is shown for a family of probability measures \((P_ \lambda)\), \[ P_ \lambda(U)=P(\xi(tT)/r\in U),\quad \lambda=r^ 2/T, \] where \(\xi(t)\), \(t\geq 0\), is a stochastic process with stationary independent increments, \(U\subseteq D[0,1]\), \(r=r(T)\), \(r/T<\infty\), \(r/T^{1/2}\to\infty\) as \(T\to\infty\). The class of sets \(U\) is defined through the Skorokhod topology or the uniform-norm topology in \(D[0,1]\). Some theorems in [J. Lynch and J. Sethuraman, ibid. 15, 610-627 (1987; Zbl 0624.60045)] appear as corollaries of the LDP for \((P_ \lambda)\). Reviewer: E.Pancheva (Sofia) Cited in 32 Documents MSC: 60F10 Large deviations 60J99 Markov processes 60E07 Infinitely divisible distributions; stable distributions Keywords:large deviation principle; stationary independent increments; Skorokhod topology; uniform-norm topology Citations:Zbl 0624.60045 PDFBibTeX XMLCite \textit{A. A. Mogulskii}, Ann. Probab. 21, No. 1, 202--215 (1993; Zbl 0769.60026) Full Text: DOI