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Multivariate exponential power Lévy processes and random fields

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  • Ma, Chunsheng

Abstract

Two multivariate exponential power Lévy processes are introduced in this paper via compound Poisson representations, which are so termed because their characteristic exponents are the linear combination of certain positive or negative power functions. They can be represented as the time changed multivariate Brownian motions using the time changes that are two exponential power subordinators, respectively. Two multivariate exponential power random fields are also proposed as elliptically contoured random fields, whose finite-dimensional characteristic functions are made up of the exponential power functions and enjoy the infinitely divisible property.

Suggested Citation

  • Ma, Chunsheng, 2023. "Multivariate exponential power Lévy processes and random fields," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000305
    DOI: 10.1016/j.spl.2023.109806
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    References listed on IDEAS

    as
    1. Huang, Steel T. & Cambanis, Stamatis, 1979. "Spherically invariant processes: Their nonlinear structure, discrimination, and estimation," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 59-83, March.
    2. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.
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