### 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 ∈ L^{2} ([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(R_{t}, sqrt(t))).

Original language | English |
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Pages (from-to) | 1690-1711 |

Number of pages | 22 |

Journal | Stochastic Processes and their Applications |

Volume | 116 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2006 Dec 1 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics

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## Cite this

*Stochastic Processes and their Applications*,

*116*(12), 1690-1711. https://doi.org/10.1016/j.spa.2006.05.001