Abstract
We introduce shift selfsimilar random sequences, as a discrete time analogue of semi-selfsimilar processes. They are also extensions of stationary random sequences. We study limit theorems for those sequences having independent increments. Our results will be a potential resource for studying Galton-Watson branching trees and diffusions on fractals. Let R be the -dimensional Euclidean space and let Z = {0 ±1 ±2 . . .}, Z+ = {0 1 2 . . .} and N = {1 2 . . .}. We consider R as the totality of -dimensional column vectors and | · | denotes the Euclidean norm in R . In this paper, we use the words “increase” and “decrease” in the wide sense allowing flatness.
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