Laws of the iterated logarithm for locally square integrable martingales

Moderate Deviations and Strassen’s Law for Additive Processes

“…Theorem (Zn S(n)) n∈N satisfies a moderate deviation principle in (D[0, 1], ⋅ ∞) with speed S(n) 2 n γ and good rate function J defined in (9).…”

“…There have been several generalizations since then; Wichura [20] and Wang [19] studied Strassen's law for additive processes and Maller [13] obtained a small-time version of Strassen's law for Lévy processes. More recently, Gao [9] proved a Strassen law for a subclass of locally square-integrable martingales. Strassen's law has a variety of applications, e. g. functional limit theorems such as the law of the iterated logarithm; see e. g. Strassen [18], Wichura [20] and Buchmann et al [2].…”