(Received October 20, 1995; revised November 8, 1996)
Abstract. We consider stochastic equations of the form X =d W1X+W2X', where (W1,W2), X and X' are independent, `=d' denotes equality in distribution, EW1+EW2 = 1 and X =d X'. We discuss existence, uniqueness and stability of the solutions, using contraction arguments and an approach based on moments. The case of {0,1}-valued W1 and constant W2 leads to a characterization of exponential distributions.
Key words and phrases: Stochastic difference equations, exponential distributions, characterization problems, contractions.