On some Fourier aspects of the construction of certain Wiener integrals

Tadahisa Funaki, Y. Hariya, F. Hirsch, M. Yor

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The existence and best L2-bounds for the Wiener type integrals ∫01 f (s) d Xs, where X ranges through a wide class of Bessel-like centered processes, and f belongs to L2 ([0, 1]), are discussed in terms of Fourier transforms associated with some characteristics of X, thus providing some unification of previous results on this topic obtained by the authors [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes and their Related Fields (2006) (in press), T. Funaki, Y. Hariya, F. Hirsch, M. Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes, Stochastic Processes and their Applications (2006) (in press)] as well as yielding new results.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalStochastic Processes and their Applications
Volume117
Issue number1
DOIs
Publication statusPublished - 2007 Jan
Externally publishedYes

Fingerprint

Bessel Process
Wiener Integral
Random processes
Markov processes
Fourier transforms
Friedrich Wilhelm Bessel
Unification
Markov Process
Stochastic Processes
Fourier transform
Range of data
Integral
Bessel process
Class

Keywords

  • Optimal bounds
  • Quadratic forms
  • Tempered distributions
  • Wiener integrals

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability
  • Modelling and Simulation

Cite this

On some Fourier aspects of the construction of certain Wiener integrals. / Funaki, Tadahisa; Hariya, Y.; Hirsch, F.; Yor, M.

In: Stochastic Processes and their Applications, Vol. 117, No. 1, 01.2007, p. 1-22.

Research output: Contribution to journalArticle

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