Strassen Laws of Iterated Logarithm for Partially Observed Processes

M. A. Lifshits () and M. Weber ()
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M. Weber: UFR de Mathématique et Informatique

Journal of Theoretical Probability, 1997, vol. 10, issue 1, 101-115

Abstract: Abstract Let a Wiener process W be observed on some nonbounded set T⊂R + . We show that alter reasonable time- and space-rescaling the correspondent interpolated sample paths converge with probability one (in the usual sense of functional laws) to some limit set in C[0, 1]. The complete description of the limit set for arbitrary T is given. Unlike the various known functional laws, this limit set is not necessarily convex. We also supply an invariance principle which permits us to obtain the same results for partially observed processes generated by the sums of i.i.d. random variables.

Keywords: Wiener process; law of the iterated logarithm; subsequences (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022694331667

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