Abstract
Ikeda and Watanabe show that (1.1) admits a weak solution and enjoys the
uniqueness-in-law property. In 2, Chitashvili shows that, indeed, the joint law of
X and W is unique (modulo the initial value of W), and that X is not measurable
with respect to W, so verifying a conjecture of Skorokhod that (1.1) does not have a
strong solution. The filtration (her) cannot be the (augmented) natural filtration of W
and the process X contains some 'extra randomness'. It is our purpose to identify this
extra randomness in terms of killing in a branching process. To this end we will study
the squared Bessel process, which can be thought of as a continuous-state branching
process, and a simple decomposition of it induced by introducing a killing term. We
will then be able to realise this decomposition in terms of the local-time processes of
X and W. Finally we will prove the following result which essentially determines the
conditional law of sticky Brownian motion given the driving Wiener process.
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