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

Sami Umut Can

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 3986-4011

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.

Keywords: Stable process; Self-similar process; Continuous additive functional; Local time; Random walk (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:12:p:3986-4011

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DOI: 10.1016/j.spa.2014.07.014

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