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A class of asymptotically self-similar stable processes with stationary increments

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  • Can, Sami Umut

Abstract

We generalize the BM-local time fractional symmetric α-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 α-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 α-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.

Suggested Citation

  • Can, Sami Umut, 2014. "A class of asymptotically self-similar stable processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3986-4011.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:3986-4011
    DOI: 10.1016/j.spa.2014.07.014
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Maejima, Makoto, 1989. "Two classes of self-similar stable processes with stationary increments," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 305-329, August.
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