※ 引述《nculeo (力歐)》之銘言：
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: 不知有無神人會呢？
: 懇求站內信求解><
: 感恩
1. dX = (2+5t+X)dt + 3dB
so u = 2+5t+X and v = 3 (standard form dX = udt + vdB)
Let g(t,x) = x^4 with dg/dt = 0, dg/dx = 4x^3, d^2g/dx^2 = 12x^2
Using Ito,
dg(t,x) = d(X^4)
= (dg/dt)dt + (dg/dx)dX + 0.5*(d^2g/dx^2)*v^2*dt
= 0 + 4X^3[(2+5t+X)dt+3dB] + 54X^2dt
= (4X^4+8X^3+54X^2+20tX^3)dt + 12X^3dB
2. 2-d BM (我用MATLAB符號表示矩陣)
v = [3 0;8Y 6]
let g(t,xy) = ysinx, dg/dt = [0 0]', [dg/dx dg/dy]' = [ycosx sinx]'
d^2g/dx^2 = [-ysinx cosx;cosx 0]
d(YsinX) = (dg/dt)dt + [dg/dx dg/dy][dX dY]
+ 0.5*v'*(d^2g/dx^2)*v*dt
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有錯請指證
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