Wiener integral for the coordinate process under the $σ$-finite measure unifying Brownian penalisations

Wiener integral for the coordinate process is defined under the $σ$-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study of Cameron--Martin formula for the $σ$-finite measure.

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