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Conditions for the existence of a generalization of Rényi divergence

Author

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  • Vigelis, Rui F.
  • de Andrade, Luiza H.F.
  • Cavalcante, Charles C.

Abstract

We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure μ is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case μ is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.

Suggested Citation

  • Vigelis, Rui F. & de Andrade, Luiza H.F. & Cavalcante, Charles C., 2020. "Conditions for the existence of a generalization of Rényi divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120304970
    DOI: 10.1016/j.physa.2020.124953
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    References listed on IDEAS

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    1. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    2. Ana Flávia P. Rodrigues & Igor M. Guerreiro & Charles Casimiro Cavalcante, 2018. "Deformed exponentials and portfolio selection," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-17, March.
    3. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    4. Rodrigues, Ana Flávia P. & Cavalcante, Charles C. & Crisóstomo, Vicente L., 2019. "A projection pricing model for non-Gaussian financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
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