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penalisation

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Wiener integral for the coordinate process underthe σ-finite measure unifying Brownian penalisations
Kouji Yano
Journal:

ESAIM: Probability and Statistics / Volume 15 / 2011

Published online by Cambridge University Press:

15 October 2010, pp. S69-S84

Print publication:

2011
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Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris 345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal. 258 (2010) 3492–3516] of Cameron-Martin formula for the σ-finite measure.