The only correction.Paths can go in either RIGHT or UPPER directions

<t>There can be a geometric interpretation here.Imagine Eucledean coordinate grid. Then it can be seen that the required number of go-game scenarios with $n$ players in each teamis the number of paths along the grid between points (0,0) and (n,n) that go in either LEFT or UPPER directionand can chan...

You seem to miss the point, sorry..When writing F(t) I do mean the argument is t, the upper limit in the integral. So F(t) is just a constant for any expression like int{... ds}.

Since W(t) = int{dW(s)} we do have F(t)W(t) = F(t) int{dW(s)} = int{F(t)dW(s)}GreekMartingale, where do you see a mistake here?

<t>A mistake seems to be here.First, in Ito's formula for H(t,W(t))=F(t)W(t) with dF/dt=f we have (H(t,x) = F(t)x; H_t(t,x) = f(t)x, H_x(t,x) = F(t), H_xx(t,x) = 0)dF(t)W(t) = f(t)W(t)dt + F(t)dW(t) (last term is correct now),which yieldsint {f(s)W(s)ds} = F(t)W(t) - int {F(s)dW(s)}.We have X = F(t)...