9.8 Let Xi be distributed as a normal with mean i and variance 2, where 1 < 2 < < n < ... ,

9.8 Let Xi be distributed as a normal with mean μi and variance σ2, where μ1 <

μ2 < ··· < μn < ... , as in the previous problem. Let a process Y = {Yi}i be defined as the sum of first i components of Xi, that is Yi = 

i j=1 Xj .

a) Construct a filtration ℱ = {ℱi}i for the stochastic process Y = {Yi}i.

b) Is Y = {Yi}i stationary? Does it have independent components?

c) Does Y = {Yi}i have stationary increments? Does it have independent increments?