On some Fourier aspects of the construction of certain Wiener integrals

T. Funaki; Y. Hariya; F. Hirsch; M. Yor

doi:10.1016/j.spa.2006.06.002

On some Fourier aspects of the construction of certain Wiener integrals

T. Funaki, Y. Hariya, F. Hirsch^*, M. Yor

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The existence and best L²-bounds for the Wiener type integrals ∫₀¹ f (s) d X_s, 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 language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	117
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2006.06.002
Publication status	Published - 2007 Jan
Externally published	Yes

Keywords

Optimal bounds
Quadratic forms
Tempered distributions
Wiener integrals

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2006.06.002

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title = "On some Fourier aspects of the construction of certain Wiener integrals",

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.",

keywords = "Optimal bounds, Quadratic forms, Tempered distributions, Wiener integrals",

author = "T. Funaki and Y. Hariya and F. Hirsch and M. Yor",

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doi = "10.1016/j.spa.2006.06.002",

language = "English",

volume = "117",

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journal = "Stochastic Processes and their Applications",

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T1 - On some Fourier aspects of the construction of certain Wiener integrals

AU - Funaki, T.

AU - Hariya, Y.

AU - Hirsch, F.

AU - Yor, M.

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

KW - Optimal bounds

KW - Quadratic forms

KW - Tempered distributions

KW - Wiener integrals

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On some Fourier aspects of the construction of certain Wiener integrals

Abstract

Keywords

ASJC Scopus subject areas

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