The corresponding results for ∆r E(R) and the radial conditional distribution of the middle point of the Brownian bridge, Ω(r;R, c, t), are shown in Fig

Following this procedure, one can straightforwardly compute the function Θ(r, R, c, t) using (43), then evaluate ∆r E(R) for two different boundary conditions: (i) mixed,∂ rP(r)| r=R +κP(R) = 0, (ii) Dirichlet,P(R) = 0 · 1944