On the construction of Wiener integrals with respect to certain pseudo-Bessel processes

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In previous papers [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes Related Fields (2006) (in press); T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes, II, Alea (2006) (in press)], the authors have shown that it is possible to define the Wiener-type integrals ∫0 1 h (s) d over(R, -)s, for every h ∈ L2 ([0, 1], d s) and (over(R, -)s) any centered Bessel process with dimension d > 1. In this paper, various conditions are stated, showing that such a construction is possible for a large class of processes indexed by two square integrable Brownian functionals. In particular, some of the results previously obtained for the Bessel processes are thus recovered, and in fact shown to extend to certain processes of the form sqrt(t) f (frac(Rt, sqrt(t))).

Original languageEnglish
Pages (from-to)1690-1711
Number of pages22
JournalStochastic Processes and their Applications
Volume116
Issue number12
DOIs
Publication statusPublished - 2006 Dec
Externally publishedYes

Fingerprint

Bessel Process
Wiener Integral
Markov processes
Friedrich Wilhelm Bessel
Markov Process
Integral
Bessel process

Keywords

  • Bessel processes
  • Gebelein's inequality
  • Hermite and Laguerre series expansions
  • Itô's representation theorem
  • Scaling property
  • Wiener integrals

ASJC Scopus subject areas

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

Cite this

On the construction of Wiener integrals with respect to certain pseudo-Bessel processes. / Funaki, Tadahisa; Hariya, Y.; Hirsch, F.; Yor, M.

In: Stochastic Processes and their Applications, Vol. 116, No. 12, 12.2006, p. 1690-1711.

Research output: Contribution to journalArticle

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