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On the spectral representation of symmetric stable processes

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  • Hardin, Clyde D.

Abstract

The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into Lp (0

Suggested Citation

  • Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:3:p:385-401
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    Citations

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    Cited by:

    1. Rutkowski, Marek, 1995. "Left and right linear innovations for a multivariate S[alpha]S random variable," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 175-184, February.
    2. Wang, Yizao & Stoev, Stilian A. & Roy, Parthanil, 2012. "Decomposability for stable processes," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1093-1109.
    3. Pipiras, Vladas & Taqqu, Murad S. & Abry, Patrice, 2003. "Can continuous-time stationary stable processes have discrete linear representations?," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 147-157, August.
    4. Sławomir Kolodyński & Jan Rosiński, 2003. "Group Self-Similar Stable Processes in R d," Journal of Theoretical Probability, Springer, vol. 16(4), pages 855-876, October.
    5. Molchanov, Ilga & Schmutz, Michael & Stucki, Kaspar, 2012. "Invariance properties of random vectors and stochastic processes based on the zonoid concept," DES - Working Papers. Statistics and Econometrics. WS ws122014, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Arijit Chakrabarty & Parthanil Roy, 2013. "Group-Theoretic Dimension of Stationary Symmetric α-Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 26(1), pages 240-258, March.
    7. Ibragimov, Ildar & Kabluchko, Zakhar & Lifshits, Mikhail, 2019. "Some extensions of linear approximation and prediction problems for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2758-2782.
    8. Vladas Pipiras & Murad S. Taqqu, 2004. "Dilated Fractional Stable Motions," Journal of Theoretical Probability, Springer, vol. 17(1), pages 51-84, January.
    9. Parthanil Roy, 2017. "Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A survey," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(4), pages 513-540, December.
    10. Pérez-Abreu, Victor & Rocha-Arteaga, Alfonso, 1997. "On stable processes of bounded variation," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 69-77, April.
    11. Roman Ger & Michael Keane & Jolanta K. Misiewicz, 2000. "On Convolutions and Linear Combinations of Pseudo-Isotropic Distributions," Journal of Theoretical Probability, Springer, vol. 13(4), pages 977-995, October.
    12. Stoev, Stilian A., 2008. "On the ergodicity and mixing of max-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1679-1705, September.
    13. Pipiras, Vladas, 2007. "Nonminimal sets, their projections and integral representations of stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1285-1302, September.
    14. Parthanil Roy & Gennady Samorodnitsky, 2008. "Stationary Symmetric α-Stable Discrete Parameter Random Fields," Journal of Theoretical Probability, Springer, vol. 21(1), pages 212-233, March.
    15. Krzysztof Burnecki, 1998. "Self-similar models in risk theory," HSC Research Reports HSC/98/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    16. Soltani, A.R. & Parvardeh, A., 2005. "Decomposition of discrete time periodically correlated and multivariate stationary symmetric stable processes," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1838-1859, November.

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