急急急!!向微積分高手求救~~推導過程問題,謝謝啦
Part II (practice with Ito).
(1)df(Wt)=(∂f/∂ Wt) *dWt+1/2*(∂ ^2f/∂ Wt^2)(dWt)^2,
with (dWt)^2=dt
(2)df(Wt,t)=(∂f/∂ t) *dt+(∂f/∂ Wt) *dWt +1/2*(∂^2f/∂Wt^2)(dWt)^2,
with (dWt)^2=dt
Given 1 and 2 from above, solve the following:
1.Using 1 and f(Wt)= Wt^2, what is the process for df(Wt)?
2.Using 1 and f(Wt)= eWt^2, what is the process for df(Wt) ?
3.Using 2 and f(Wt)= Wt^2 -t, what is the process for df(Wt)?
4.Using 2 and f(Wt)= Wt^3 -3tWt, what is the process for df(Wt)?
5.Using 2 and f(Wt)= Wt^4 -6tWt^2 +3t^2, what is the process for df(Wt)?