On recurrence for self-similar additive processes. (English) Zbl 0971.60043
A stochastic process \(\{X_t: t \geq 0\}\) on \(R^d\) is called a self-similar additive process with exponent \(H > 0\) if it is \(H\)-self-similar, has independent increments and càdlàg sample paths. Unlike stable Lévy processes, additive processes are not assumed to be time-homogeneous. The author proves some sufficient conditions for self-similar additive processes to be recurrent.
Reviewer: Yimin Xiao (East Lansing)
MSC:
| 60G18 | Self-similar stochastic processes |
| 60J25 | Continuous-time Markov processes on general state spaces |
References:
| [1] | K. SATO, Processes with Independent Increments, Kinokuniya, 1990 (in Japanese). · Zbl 0817.60038 |
| [2] | K. SATO, Self-similar processes with independent increments, Probab. Theory Related Fields, 89 (1991), 285-300 · Zbl 0725.60034 · doi:10.1007/BF01198788 |
| [3] | K. SATO AND K. YAMAMURO, On selfsimilar and semi-selfsimilar processes with independen increments, J. Korean Math. Soc, 35 (1998), 207-224. · Zbl 0902.60032 |
| [4] | T. WATANABE, Sample function behavior of increasing processes of class L, Probab. Theor Related Fields, 104 (1996), 349-374. · Zbl 0849.60036 · doi:10.1007/BF01213685 |
| [5] | K. YAMAMURO, Transience conditions for self-similar additive processes, in J. Math. Soc Japan, 52 (2000), 343-362. · Zbl 0963.60033 · doi:10.2969/jmsj/05220343 |
| [6] | M. YAMAZATO, Unimodality of infinitely divisible distribution functions of class L, Ann Probab., 6 (1978), 523-531. · Zbl 0394.60017 · doi:10.1214/aop/1176995474 |
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