- A class of asymptotically self-similar stable processes with stationary increments
- Stochastic Processes and their Applications
- Volume | Issue number
- 124 | 12
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
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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