Аннотация:
We develop a Brownian penalisation procedure related to weight processes $(F_t)$ of
the type: $F_t:=f(I_t, S_t)$ where $f$ is a bounded function with compact support and
$S_t$ (resp. $I_t$) is the one-sided maximum (resp. minimum) of the Brownian motion
up to time $t.$ Two main cases are treated: either $F_t$t is the indicator function of
$\{I_t\geq\alpha, S_t\leq\beta\}$ or $F_t$t is null when $\{S_t-I_t>c\}$ for some $c>0.$ Then we apply
these results to some kind of asymptotic Skorokhod embedding problem.
Ключевые слова:Skorokhod’s problem, penalisation, one-sided maximum and minimum,
Laplace’s method.