diffusion method

Maruyama T & Kimura M 1971 Some methods for treating continuous stochastic process in population genetics. Jpn J Genet 46:407-410.

• let us calculate the sum of heterozygosity for the paths leading to fixation
• H₁⁽¹⁾(p) = F₁⁽¹⁾(p) / p = (4N_e / 3)(1 − p²)

• if we put f(x) = δ(x − y), where δ(·) is the Dirac delta function, then, the unique solution, denoted by Φ(p, y) of equation (3) with boundary conditions Φ(0, y) = Φ(1, y) = 0 gives the total sojourn time at y for the paths starting from p
• this is equivalent to "the transient function" t(x) of Ewens (1969), and also to the steady flux distribution with ν_m = 1 given by Kimura (1969)