  In this paper, we establish a probabilistic representation for two
integration by parts formulas, one being of Bismut-Elworthy-Li's type, for the
marginal law of a one-dimensional diffusion process killed at a given level.
These formulas are established by combining a Markovian perturbation argument
with a tailor-made Malliavin calculus for the underlying Markov chain structure
involved in the probabilistic representation of the original marginal law.
Among other applications, an unbiased Monte Carlo path simulation method for
both integration by parts formula stems from the previous probabilistic
representations.
