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Hi, can someone please provide some guidance on how i should go about finding the stationary distribution of:

[tex]X_t = [/tex] [tex] \rho X_{t-1} + \epsilon_t[/tex], [tex]X_0 = 0 [/tex]and [tex]|\rho|<1[/tex]

where [tex]\epsilon_1, \epsilon_2, \cdots[/tex] are all independent N(0,1)..

i have no idea what to do, so here's my attempt which i know to be completely wrong:

suppose,

[tex]Var(X_1) = \rho \sigma^2 < \infty [/tex]

[tex] Var(X_2) = \rho\sigma^2 + 1 [/tex]

[tex] \vdots [/tex]

[tex]Var(X_{n+1}) = \rho\sigma^2 + t [/tex]

As [tex] t \rightarrow \infty, Var(X_{n+1} = \rho \sigma^2 + t [/tex] ????????

yeah im very sure im not doing it right... Can someone please help me out?

[tex]X_t = [/tex] [tex] \rho X_{t-1} + \epsilon_t[/tex], [tex]X_0 = 0 [/tex]and [tex]|\rho|<1[/tex]

where [tex]\epsilon_1, \epsilon_2, \cdots[/tex] are all independent N(0,1)..

i have no idea what to do, so here's my attempt which i know to be completely wrong:

suppose,

[tex]Var(X_1) = \rho \sigma^2 < \infty [/tex]

[tex] Var(X_2) = \rho\sigma^2 + 1 [/tex]

[tex] \vdots [/tex]

[tex]Var(X_{n+1}) = \rho\sigma^2 + t [/tex]

As [tex] t \rightarrow \infty, Var(X_{n+1} = \rho \sigma^2 + t [/tex] ????????

yeah im very sure im not doing it right... Can someone please help me out?

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