A note on the stationarity of a threshold first-order bilinear process.

In the present note we study the threshold first-order bilinear model X(t) = aX(t - 1) + (b(1) 1({x(t-1)<c}) + b(2) 1({x(t-1)greater than or equal to c}))X(t-1) e(t - 1) + e(t), t is an element of N, where {e(t), t is an element of N} is a sequence of i.i.d, absolutely continuous random variables, X(0) is a given random variable and a, b(1), b(2) and c are real numbers. Under suitable conditions on the coefficients and lower semicontinuity of the densities of the noise sequence, we provide sufficient conditions for the existence of a stationary solution process to the present model and of its finite moments of order p.