Wiener integral for the coordinate process under the<i>σ</i>-finite measure unifying Brownian penalisations

Yano, Kouji

doi:10.1051/ps/2010024

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2010

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“…(To avoid confusion, we give the following remark: In [3] and [4], the Wiener integral means the integral with respect to the Wiener measure.) The author has proved in his recent work [18] that this Wiener integral is well-defined if f ∈ L 2 (ds) ∩ L 1 ( ds 1+ √ s ), i.e., (1.6)…”

Section: Introductionmentioning

confidence: 99%

Cameron–Martin formula for the σ-finite measure unifying Brownian penalisations

Yano¹

2010

Journal of Functional Analysis

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Quasi-invariance under translation is established for the σ -finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor [J. Najnudel, B. Roynette, M. Yor, A remarkable σ -finite measure on C(R + , R) related to many Brownian penalisations, C. R. Math. Acad. Sci. Paris 345 (8) (2007) 459-466]. For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes. II, ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006) 225-240 (electronic)], plays a key role.

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Section: Introductionmentioning

confidence: 99%