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Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , 345 (2007) 459–466] and [Najnudel , 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, 258 (2010) 3492–3516] of Cameron-Martin formula for the -finite measure.
Wiener integral for the coordinate process
is defined under the -finite measure unifying Brownian penalisations,
which has been introduced by [Najnudel ,
(2007) 459–466] and [Najnudel ,
. 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,
(2010) 3492–3516] of Cameron-Martin formula
for the -finite measure.
Penalisation involving the one-sided supremum for a stable Lévy process with index ∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
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