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Let W0+(I), 0 ), v > 0, be its local time at level t>. Starting from a representation of the density of /0+(t>) as a complex integral we derive an explicit form of this density, written as an infinite series involving the n-fold convolution of known densities. Finally the result is used as an alternative check of Knight's result on the same topic. 1. Introduction. In (2) and (4) an expression is given for the distribution of Brownian excursion local time /0+(u), v > 0. In these papers this distribution is represented as a complex integral and it is easily verified that this representation is equivalent to the double Laplace transform given in Formula (3.17) of (3) (for this verification see §2). Although both relations seem difficult to invert (cf. (3, final part of §3)) we have succeeded in giving an explicit form for the density of /0+(u), v > 0, as an infinite series involving the n-fold convolution of known densities. In the final part of this note it is shown that our result agrees with that of Knight (cf. (5)). To read this note no knowledge of complex integration other than the inversion theorem for Laplace transforms is necessary.

On the explicit form of the density of Brownian excursion local time