We can combine these equations and arrive at the famous Einstein-Smoluchenski-Kolmogorov-Chapman (ESKC) relation
W(xt|x0t0)=∫∞−∞W(x,t|x′,t′)W(x′,t′|x0,t0)dx′.We can replace the spatial dependence with a dependence upon say the velocity (or momentum), that is we have
W(v,t|v0,t0)=∫∞−∞W(v,t|v′,t′)W(v′,t′|v0,t0)dx′.