pmpm=pm+dpmdy dy-dpmdt dt+(1/2) d2pmdy2 (dy^2); (* this is (SuperMinus[ϕ])(y'+δy,t'-δt) *)
ppmm=pp-dppdy dy-dppdt dt+(1/2)d2ppdy2 (dy^2); (* this is (SuperPlus[ϕ])(y'-δy,t'-δt) *)
pp0m=pp-dppdt dt; (* this is (SuperPlus[ϕ])(y',t'-δt) *)
pm0m=pm-dpmdt dt; (* this is (SuperMinus[ϕ])(y',t'-δt) *)

ppm=p+dpdy dy - dpdt dt +(1/2) d2pdy2 (dy^2); (* this is p(y,t;y'+δy,t'-δt) *)
p0m=p-dpdt dt; (* this is p(y,t;y',t'-δt) *)
pmm=p-dpdy dy-dpdt dt+(1/2) d2pdy2 (dy^2); (* this is p(y,t;y'-δy,t'-δt) *)

(* the right-hand-side of the derivation of the forward Kolmogorov equation *)
wProd=pmpm ppm+(1-pm0m-pp0m) p0m+ppmm pmm//Expand

wProdDT=wProd /.{dy->(dt^(1/2))}

(* extract out the coefficients of dt *)
Coefficient[wProdDT,dt,0]
Coefficient[wProdDT,dt,(1/2)]
Coefficient[wProdDT,dt]
Coefficient[wProdDT,dt,(3/2)]
Coefficient[wProdDT,dt,2]