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Sojourns and extremes of Fourier sums and series with random coefficients

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  • Berman, Simeon M.

Abstract

Let X(t) be the trigonometric polynomial [Sigma]kj=0aj(Ut cos jt+Vj sin jt), -[infinity] u}, and M(t) = max{X(s): 0[less-than-or-equals, slant]s[less-than-or-equals, slant]t}. Limit theorems for Lt(u) and P(M(t) > u) for u-->[infinity] are obtained under the hypothesis that the distribution of the random norm ([Sigma]kj=0(U2j+V2j))1 2 belongs to the domain of attraction of the extreme value distribution exp{ e-2}. The results are also extended to the random Fourier series (k=[infinity]).

Suggested Citation

  • Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    • Handle: RePEc:eee:spapps:v:15:y:1983:i:3:p:213-238
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    Cited by:

    1. Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.
    2. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
    3. Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    4. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    5. Hashorva, Enkelejd, 2010. "Asymptotics of the norm of elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 926-935, April.
    6. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    7. Hashorva, Enkelejd, 2007. "Extremes of conditioned elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1583-1591, September.

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