|Apr27-09, 08:09 AM||#1|
Difference equation with non-linear term
I can't figure out how to approach the following difference equation:
where a, b are constants, e_t is a known function and f(x_t-1) is a convex, u-shaped function that goes through the origin.
(Sorry Tex would not want to work)
To begin with, I considered f linear and solved the equation. Exactly one of the roots of the corresponding homogenous equation lies within the unit circle, so I set the free coefficients in the general solution to zero to obtain a bounded solution and derive the particular solution.
Does anyone know a way to treat a nonlinear function f?
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