## [數學]向微積分高手求救!!微積分難題!!!

### [數學]向微積分高手求救!!微積分難題!!!

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)?

himax67

kunfrank

### Re: [數學]向微積分高手求救!!微積分難題!!!

himax67 寫到:

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)?

(1)2Wt dWt +dt
(2)2eWt dWt +edt
(3) 2Wt dWt
(4)3(Wt^2-1) dWt
(5)4(Wt^3 -3tWt)dWt

guest