Abstract.
We show that fractional Brownian motions with index in (0,1] satisfy a remarkable property: their squares are infinitely divisible. We also prove that a large class of Gaussian processes are sharing this property. This property then allows the construction of two-parameters families of processes having the additivity property of the squared Bessel processes.
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Received: 1 April 2002 / Revised version: 7 September 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 60E07, 60G15, 60J25, 60J55
Key words or phrases: Gaussian processes – Infinite divisibility – Markov processes
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Eisenbaum, N. On the infinite divisibility of squared Gaussian processes. Probab Theory Relat Fields 125, 381–392 (2003). https://doi.org/10.1007/s00440-002-0245-z
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DOI: https://doi.org/10.1007/s00440-002-0245-z
Keywords
- Brownian Motion
- Large Class
- Gaussian Process
- Additivity Property
- Fractional Brownian Motion