Limit theorems related to a class of operator semi-selfsimilar processes
Vol. 12 (2005), No. 1, Page 111--140.
Saigo, Tatsuhiko; Takahashi, Hiroshi
Limit theorems related to a class of operator semi-selfsimilar processes
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Abstract:
We construct a class of operator semi-selfsimilar processes with stationary increments as limiting processes of scaled partial sums of some random walks in random scenery, studied by Kesten and Spitzer for selfsimilar processes' case. In the present paper, we generalize previous works related to problems of random walks in random scenery in the following two senses; we assume (i) random sceneries belong to the domain of partial normal attraction of strictly operator semi-stable distributions, and (ii) random walks belong to the domain of partial normal attraction of strictly semi-stable distributions. To consider such a problem, we also study local limit theorems related to semi-stable L\'evy processes.
Mathematics Subject Classification (1991): Primary 60G18; Secondary 60G37, 60G50, 60F05.
Mathematical Reviews Number: MR2126788
Received: 2004-12-07
