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Selfdecomposability and selfsimilarity: A concise primer

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  • Cufaro Petroni, Nicola

Abstract

We summarize the relations among three classes of laws: infinitely divisible, selfdecomposable and stable. First we look at them as the solutions of the Central Limit Problem; then their role is scrutinized in relation to the Lévy and the additive processes with an emphasis on stationarity and selfsimilarity. Finally we analyze the Ornstein–Uhlenbeck processes driven by Lévy noises and their selfdecomposable stationary distributions, and we end with a few particular examples.

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  • Cufaro Petroni, Nicola, 2008. "Selfdecomposability and selfsimilarity: A concise primer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1875-1894.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:8:p:1875-1894
    DOI: 10.1016/j.physa.2007.11.036
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    References listed on IDEAS

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    1. McCauley, Joseph L. & Gunaratne, Gemunu H. & Bassler, Kevin E., 2007. "Hurst exponents, Markov processes, and fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 1-9.
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    Cited by:

    1. Piergiacomo Sabino & Nicola Cufaro Petroni, 2022. "Fast simulation of tempered stable Ornstein–Uhlenbeck processes," Computational Statistics, Springer, vol. 37(5), pages 2517-2551, November.
    2. Sandya N. Kumari, 2020. "L¨¦vy Processes in Gold Option Modeling," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 12(2), pages 1-65, February.

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