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Asymptotic normality of sums of Hilbert space valued random elements

  • Alfredas Račkauskas EMAIL logo
Veröffentlicht/Copyright: 4. Dezember 2019
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Georgian Mathematical Journal
Aus der Zeitschrift Georgian Mathematical Journal Band 28 Heft 3

Abstract

We investigate the asymptotic normality of distributions of the sequence ∑k∈ℤun,k⁢Xk, n∈ℕ, where (Xk,k∈ℤ) either is a sequence of i.i.d. random elements or constitutes a linear process with i.i.d. innovations in a separable Hilbert space. The weights (un,k) are in general a family of linear bounded operators. This model includes operator weighted sums of Hilbert space valued linear processes, operator-wise discounted sums in a Hilbert space as well some extensions of classical summation methods.

Keywords: Summation methods; Hilbert space; asymptotic normality; linear processes
MSC 2010: 60B12; 60F05

Funding source: Lietuvos Mokslo Taryba

Award Identifier / Grant number: S-MIP-17-76

Funding statement: The research was supported by the Research Council of Lithuania, grant no. S-MIP-17-76.

References

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Received: 2018-01-08
Revised: 2019-03-21
Accepted: 2019-04-01
Published Online: 2019-12-04
Published in Print: 2021-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On “On derivations and commutativity of prime rings with involution”
  3. Some properties of rings and near-rings with derivations and generalized derivations
  4. Complex interpolation of the predual of Morrey spaces over measure spaces
  5. Meromorphic functions sharing unique range sets with one or two elements
  6. Menger algebras of k-commutative n-place functions
  7. Steklov eigenvalue problem with a-harmonic solutions and variable exponents
  8. Singular integral operators in some variable exponent Lebesgue spaces
  9. Asymptotic relations involving 𝑑-orthogonal polynomials
  10. BMO-type estimates of Riesz transforms associated with generalized Schrödinger operators
  11. On zero-divisors of semimodules and semialgebras
  12. Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition
  13. On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse
  14. On the classification of endomorphisms on infinite-dimensional vector spaces
  15. Asymptotic normality of sums of Hilbert space valued random elements
  16. A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
  17. A note on the strong summability of two-dimensional Walsh–Fourier series
  18. On the theory and practice of thin-walled structures
https://doi.org/10.1515/gmj-2019-2075
Schlagwörter für diesen Artikel
Summation methods; Hilbert space; asymptotic normality; linear processes

Artikel in diesem Heft

  1. Frontmatter
  2. On “On derivations and commutativity of prime rings with involution”
  3. Some properties of rings and near-rings with derivations and generalized derivations
  4. Complex interpolation of the predual of Morrey spaces over measure spaces
  5. Meromorphic functions sharing unique range sets with one or two elements
  6. Menger algebras of k-commutative n-place functions
  7. Steklov eigenvalue problem with a-harmonic solutions and variable exponents
  8. Singular integral operators in some variable exponent Lebesgue spaces
  9. Asymptotic relations involving 𝑑-orthogonal polynomials
  10. BMO-type estimates of Riesz transforms associated with generalized Schrödinger operators
  11. On zero-divisors of semimodules and semialgebras
  12. Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition
  13. On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse
  14. On the classification of endomorphisms on infinite-dimensional vector spaces
  15. Asymptotic normality of sums of Hilbert space valued random elements
  16. A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
  17. A note on the strong summability of two-dimensional Walsh–Fourier series
  18. On the theory and practice of thin-walled structures
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