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Firstly, we compute the distribution function for the hitting time of alinear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by areflecting Brownian motion. The main tool hereby is Doob's formula which givesthe probability that Brownian motion started inside a wedge does not hit thiswedge. Other key ingredients are the time inversion property of Brownian motionand the time reversal property of diffusion bridges. Secondly, this methodologycan also be applied for the three dimensional Bessel process. Thirdly, weconsider Bessel bridges from 0 to 0 with dimension parameter $\delta>0$ andshow that the probability that such a Bessel bridge crosses an affine boundaryis equal to the probability that this Bessel bridge stays below some fixedvalue.

On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes