A class of asymptotically self-similar stable processes with stationary increments
| Authors |
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| Publication date |
2014
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| Journal |
Stochastic Processes and their Applications
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| Volume | Issue number |
124 | 12
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| Pages (from-to) |
3986-4011
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| Organisations |
-
Faculty of Economics and Business (FEB) - Amsterdam School of Economics Research Institute (ASE-RI)
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| Abstract |
We generalize the BM-local time fractional symmetric image-stable motion introduced in Cohen and Samorodnitsky (2006) by replacing the local time with a general continuous additive functional (CAF). We show that the resulting process is again symmetric image-stable with stationary increments. Depending on the CAF, the process is either self-similar or lies in the domain of attraction of the BM-local time fractional symmetric image-stable motion. We also show that the process arises as a weak limit of a discrete "random rewards scheme" similar to the one described by Cohen and Samorodnitsky.
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| Document type |
Article
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| Language |
English
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| Published at |
https://doi.org/10.1016/j.spa.2014.07.014
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