Random inhomogeneous binary recurrences

Abstract. The random inhomogeneous binary recurrence \((G_n)_{n=0}^\infty\) is defined by the initial values \(G_0=0\), \(G_1=1\), and by the recurrence rule \(G_n=AG_{n-1}+BG_{n-2}+w_{n-2}\), where \(A,B\) are given real numbers, and \((w_n)_{n=0}^\infty\) is a random sequence with \(s\ge2\) possible real values. In this work, we investigate the properties of the sequence \((G_n)\).