Summary
Under the assumption of the convergence of partial sum processesZ n (t) of i.i.d. random variables to an α-stable Lévy processZ(σ)(t), 0<α≦2, the convergence of weighted sums ∫f n (u)dZ n (u) to ∫f(u)dZ (α)(u) is studied. The general convergence result is then applied to examine the domain of attraction of the fractional stable process.
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Supported in part by Grant-in-Aid for Scientific Research, No. 60740103, Ministry of Education, Science and Culture
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Kasahara, Y., Maejima, M. Weighted sums of I.I.D. Random variables attracted to integrals of stable processes. Probab. Th. Rel. Fields 78, 75–96 (1988). https://doi.org/10.1007/BF00718037
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DOI: https://doi.org/10.1007/BF00718037
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Convergence Result
- Stable Process