Abstract.
Let α? (1,2) and X α be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average
where is a standard Lebesgue space, is some measurable function and M α is a SαS random measure on X ×ℝ with the control measure m α (dx, du) = μ(dx)du. We show that if X α is self-similar, then it is determined by a nonsingular flow, a related cocycle and a semi-additive functional. By using the Hopf decomposition of the flow into its dissipative and conservative components, we establish a unique decomposition in distribution of X α into two independent processes
where the process X α D is determined by a nonsingular dissipative flow and the process X α C is determined by a nonsingular conservative flow. In this decomposition, the linear fractional stable motion, for example, is determined by a conservative flow.
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Received: 20 June 2000 / Revised version: 6 September 2001 / Published online: 14 June 2002
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Pipiras , V., Taqqu, M. Decomposition of self-similar stable mixed moving averages. Probab Theory Relat Fields 123, 412–452 (2002). https://doi.org/10.1007/s004400200196
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DOI: https://doi.org/10.1007/s004400200196