A class of asymptotically self-similar stable processes with stationary increments |
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Authors: | Sami Umut Can |
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Affiliation: | University of Amsterdam, Faculty of Economics & Business, Section Actuarial Science, Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands |
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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. |
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Keywords: | 60G18 60G52 60G50 |
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