Let X0 ≡ 0, and consider a stochastic recursion of the form Xn+1 =c+ρXn +σεn+1 for...

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Question

Let X0 ≡ 0, and consider a stochastic recursion of the form Xn+1 =c+ρXn +σεn+1 for...

Let X0 ≡ 0, and consider a stochastic recursion of the form
Xn+1 =c+ρXn +σεn+1

for all n ≥ 0, where c, σ > 0, |ρ| < 1, and ε1, ε2, ... are iid N(0, 1). Compute the quantities:

a.) lim n→∞ EXn.

b.) lim n→∞ var Xn.

math Statistics-And-Probability

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Answer 1

Answer #1

Continuing in this way n times, we get

(X0 = 0)

a)

(By Sum of infinite geometric series)

b)

(By Sum of infinite geometric series)

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Answer 2

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Let X0 ≡ 0, and consider a stochastic recursion of the form Xn+1 =c+ρXn +σεn+1 for...