theorem steady_state_variance (M sig_new : ℝ) (hM : 1 < M) :
varianceRecurrence (M * sig_new) M sig_new = M * sig_new := by
simp only [varianceRecurrence]
have hMne : M ≠ 0 := ne_of_gt (by linarith)
field_simp
ringResults 86-92: Endogenous Variance Dynamics