Abstract
In terms of the two-parameter Mittag-Leffler function with specified parameters, this paper introduces the Mittag-Leffler vector random field through its finite-dimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two parameters of the Mittag-Leffler function equal 1. Having second-order moments, a Mittag-Leffler vector random field is characterized by its mean function and its covariance matrix function, just like a Gaussian one. In particular, we construct direct and cross covariances of Mittag-Leffler type for such vector random fields.
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Acknowledgments
This work is partly supported by U.S. Department of Energy under Grant DE-SC0005359. The author is grateful to Professor N.N. Leonenko for helpful discussions regarding the Mittag-Leffler function, and to an anonymous referee for valuable comments and suggestions that led to a considerably improved presentation of this paper.
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Ma, C. Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions. Ann Inst Stat Math 65, 941–958 (2013). https://doi.org/10.1007/s10463-013-0398-9
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DOI: https://doi.org/10.1007/s10463-013-0398-9