Decomposition of self-similar stable mixed moving averages

@article{Pipiras2002DecompositionOS,
  title={Decomposition of self-similar stable mixed moving averages},
  author={Vladas Pipiras and Murad S. Taqqu},
  journal={Probability Theory and Related Fields},
  year={2002},
  volume={123},
  pages={412-452}
}
Abstract. Let α? (1,2) and Xα 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 Mα is a SαS random measure on X ×ℝ with the control measure mα(dx, du) = μ(dx)du. We show that if Xα 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… 
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