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

✍ Scribed by Nunzio Cappuccio; Marco Ferrante; Giovanni Fonseca

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 312 KB
• Volume: 40
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00144-8

✦ Synopsis

In the present note we study the threshold first-order bilinear model

where {e(t), t E ~} is a sequence of i.i.d, absolutely continuous random variables, X(0) is a given random variable and a, bL, b2 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. (~