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由 **guest** 於星期五七月 27, 2007 4:32 pm

himax67 寫到:#ed_op#DIV#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /#ed_cl##ed_op#o:p#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#P#ed_cl#急急急!!向微積分高手求救~~推導過程問題,謝謝啦#ed_op#BR#ed_cl##ed_op#BR#ed_cl#Part II (practice with Ito).#ed_op#BR#ed_cl##ed_op#BR#ed_cl#(1)df(Wt)=(∂f/∂ Wt) *dWt+1/2*(∂ ^2f/∂ Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl#(2)df(Wt,t)=(∂f/∂ t) *dt+(∂f/∂ Wt) *dWt +1/2*(∂^2f/∂Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl##ed_op#BR#ed_cl#Given 1 and 2 from above, solve the following:#ed_op#BR#ed_cl##ed_op#BR#ed_cl#1.Using 1 and f(Wt)= Wt^2, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.Using 1 and f(Wt)= eWt^2, what is the process for df(Wt) ?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#3.Using 2 and f(Wt)= Wt^2 -t, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#4.Using 2 and f(Wt)= Wt^3 -3tWt, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#5.Using 2 and f(Wt)= Wt^4 -6tWt^2 +3t^2, what is the process for df(Wt)?#ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl#

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

由 **kunfrank** 於星期四七月 12, 2007 4:55 pm

看不明你的題目

由 **himax67** 於星期二七月 10, 2007 11:50 pm

#ed_op#DIV#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /#ed_cl##ed_op#o:p#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#P#ed_cl#急急急!!向微積分高手求救~~推導過程問題,謝謝啦#ed_op#BR#ed_cl##ed_op#BR#ed_cl#Part II (practice with Ito).#ed_op#BR#ed_cl##ed_op#BR#ed_cl#(1)df(Wt)=(∂f/∂ Wt) *dWt+1/2*(∂ ^2f/∂ Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl#(2)df(Wt,t)=(∂f/∂ t) *dt+(∂f/∂ Wt) *dWt +1/2*(∂^2f/∂Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl##ed_op#BR#ed_cl##ed_op#BR#ed_cl#Given 1 and 2 from above, solve the following:#ed_op#BR#ed_cl##ed_op#BR#ed_cl#1.Using 1 and f(Wt)= Wt^2, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.Using 1 and f(Wt)= eWt^2, what is the process for df(Wt) ?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#3.Using 2 and f(Wt)= Wt^2 -t, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#4.Using 2 and f(Wt)= Wt^3 -3tWt, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#5.Using 2 and f(Wt)= Wt^4 -6tWt^2 +3t^2, what is the process for df(Wt)? #ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: right" align=right#ed_cl##ed_op#SPAN style="POSITION: relative; TOP: 15pt; mso-text-raise: -15.0pt"#ed_cl##ed_op#?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /#ed_cl##ed_op#v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"#ed_cl##ed_op#v:stroke joinstyle="miter"#ed_cl##ed_op#/v:stroke#ed_cl##ed_op#v:formulas#ed_cl##ed_op#v:f eqn="if lineDrawn pixelLineWidth 0"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="sum @0 1 0"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="sum 0 0 @1"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @2 1 2"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @3 21600 pixelWidth"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @3 21600 pixelHeight"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="sum @0 0 1"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @6 1 2"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @7 21600 pixelWidth"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="sum @8 21600 0"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="prod @7 21600 pixelHeight"#ed_cl##ed_op#/v:f#ed_cl##ed_op#v:f eqn="sum @10 21600 0"#ed_cl##ed_op#/v:f#ed_cl##ed_op#/v:formulas#ed_cl##ed_op#v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"#ed_cl##ed_op#/v:path#ed_cl##ed_op#o:lock aspectratio="t" v:ext="edit"#ed_cl##ed_op#/o:lock#ed_cl##ed_op#/v:shapetype#ed_cl##ed_op#v:shape id=_x0000_i1025 style="WIDTH: 270pt; HEIGHT: 36pt" o:ole="" type="#_x0000_t75"#ed_cl##ed_op#v:imagedata o:title="" src="file:///C:\DOCUME~1\葉家榮\LOCALS~1\Temp\msohtml1\ 01\clip_image001.wmz"#ed_cl##ed_op#/v:imagedata#ed_cl##ed_op#/v:shape#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl#

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Re: [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!!!

(請將產生的程式碼，剪貼至上方文章區！)
[quote="guest"][quote="himax67"]#ed_op#DIV#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /#ed_cl##ed_op#o:p#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"#ed_cl##ed_op#P#ed_cl#急急急!!向微積分高手求救~~推導過程問題,謝謝啦#ed_op#BR#ed_cl##ed_op#BR#ed_cl#Part II (practice with Ito).#ed_op#BR#ed_cl##ed_op#BR#ed_cl#(1)df(Wt)=(∂f/∂ Wt) dWt+1/2(∂ ^2f/∂ Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl#(2)df(Wt,t)=(∂f/∂ t) dt+(∂f/∂ Wt) dWt +1/2*(∂^2f/∂Wt^2)(dWt)^2, #ed_op#BR#ed_cl#with (dWt)^2=dt #ed_op#BR#ed_cl##ed_op#BR#ed_cl#Given 1 and 2 from above, solve the following:#ed_op#BR#ed_cl##ed_op#BR#ed_cl#1.Using 1 and f(Wt)= Wt^2, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.Using 1 and f(Wt)= eWt^2, what is the process for df(Wt) ?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#3.Using 2 and f(Wt)= Wt^2 -t, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#4.Using 2 and f(Wt)= Wt^3 -3tWt, what is the process for df(Wt)?#ed_op#BR#ed_cl##ed_op#BR#ed_cl#5.Using 2 and f(Wt)= Wt^4 -6tWt^2 +3t^2, what is the process for df(Wt)?#ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl#[/quote]#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#這不就是Ito's Lemma嗎？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(1)2Wt dWt +dt#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(2)2eWt dWt +edt#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(3) 2Wt dWt #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(4)3(Wt^2-1) dWt #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(5)4(Wt^3 -3tWt)dWt#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#事實上這些都是Ito process，不過我都用隨機積分那邊來定義。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#它只是要你套Ito的微分公式而已。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl# [/quote]