Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions |
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| Authors: | Ken-iti Sato Kouji Yamamuro |
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| Institution: | (1) Hachiman-yama 1101-5-103, Tenpaku-ku, Nagoya, 468-0074, Japan;(2) Aichi Konan College, Takaya-cho, Konan, 483-8086, Japan |
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| Abstract: | For any stable distribution  on the line, recurrence-transience of the selfsimilar additive process {X
t
, t 0} with  (X
1)= is determined. Comparison with the stable Lévy process {Y
t
,t0} with (Y
1)= is made: if is not strictly stable, then {Y
t
} is transient but {X
t
} is recurrent except the obviously transient case of monotone sample functions. |
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| Keywords: | recurrence-transience additive processes stable distributions |
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