1-) let fCE) be a differentiasle funckion. Show that pCe) dwce) = cA)wC6) - ecalwca) 3) Solue the following stoche stic differential equation: dx CE) = B xCE) + adwCt) xC0) = Then use t he resulle of the previous exercise () to show thats -p Ct-s) XCE) = Xoe + Lw CE). %3D
1-) let fCE) be a differentiasle funckion. Show that pCe) dwce) = cA)wC6) - ecalwca) 3) Solue the following stoche stic differential equation: dx CE) = B xCE) + adwCt) xC0) = Then use t he resulle of the previous exercise () to show thats -p Ct-s) XCE) = Xoe + Lw CE). %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.) Let fCE) bea differentiasle function. Show that,
%3D
9) Solue the folllouing stochestic differential equation:
dx CE) =
B xCE)
+ adw Ct)
xCo) =
Then use the resulle of the previous exercise () to show thats
7.
-p Ct- s)
XCE) = x,e' + duCE) -CawCL)
WCE)e
%3D
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Transcribed Image Text:4. Consider the following function:
I – 2, -2 < I < -1
-1< r<1
f(2) =
%3D
2 – 1,
1<r<2.
(i) Sketch the graph of f and find its Fourier series on [-2, 2).
(ii) Use the obtained series to deduce that:
1
and 2k – 1)“
(2k
1)2
8
96
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