Here, the kernel k α α ( t ) and the WT-PDF ψ ψ α α ( t ) are related in Laplace space, k ¯ ¯ α α ( s ) = s ψ ψ ¯ ¯ α α ( s ) 1 − − ψ ψ ¯ ¯ α α ( s ) . (The Laplace transform of a function f ( t ) reads, f ¯ ¯ ( s ) = ∫ ∫ 0 ∞ ∞ f ( t ) e − − s t d t .) The reflecting boundary conditions accompanied Eq. (8) are obtained when convoluting the boundary conditions of a Brownian file with the kernel k α α ( t ) , where here and in a Brownian file the initial conditions are identical.