sm8_16

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Problem 8.16 Is the discrete-time process {Yn: n = 1,2,…} defined by: Y0 = 0 and 
 
nnn WYY +=+ α1 , 
 
a Gaussian process, if Wn is Gaussian? 
 
Solution 
 
(Proof by mathematical induction.) The first term 001 WYY += α is Gaussian since 00 =Y 
and are Gaussian. The second term 0W 112 WYY +=α is Gaussian since and are 
Gaussian. Assume is Gaussian. Then 
1Y 1W
nY nnn WYY +=+ α1 is Gaussian since and are 
both Gaussian. 
nY nW
 
 
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