TY - JOUR

T1 - Strassen Laws of Iterated Logarithm for Partially Observed Processes

AU - Lifshits, M. A.

AU - Weber, M.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Let a Wiener process W be observed on some nonbounded set T ⊂ R + . We show that after 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.

AB - Let a Wiener process W be observed on some nonbounded set T ⊂ R + . We show that after 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.

KW - Law of the iterated logarithm

KW - Subsequences

KW - Wiener process

UR - http://www.scopus.com/inward/record.url?scp=0031504080&partnerID=8YFLogxK

U2 - 10.1023/A:1022694331667

DO - 10.1023/A:1022694331667

M3 - Article

AN - SCOPUS:0031504080

VL - 10

SP - 101

EP - 115

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 1

ER -