[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!!!

himax67 於 星期二 七月 10, 2007 11:50 pm


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)?


himax67
初學者
初學者
 
文章: 1
註冊時間: 2007-07-10

kunfrank 於 星期四 七月 12, 2007 4:55 pm


看不明你的題目

kunfrank
初學者
初學者
 
文章: 2
註冊時間: 2007-07-04

Re: [數學]向微積分高手求救!!微積分難題!!!

guest 於 星期五 七月 27, 2007 4:32 pm


himax67 寫到:

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)?

 
這不就是Ito's Lemma嗎?
 
(1)2Wt dWt +dt
(2)2eWt dWt +edt
(3) 2Wt dWt
(4)3(Wt^2-1) dWt
(5)4(Wt^3 -3tWt)dWt
 
事實上這些都是Ito process,不過我都用隨機積分那邊來定義。
它只是要你套Ito的微分公式而已。

guest
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