A note on the existence of solutions to a stochastic recurrence equation
نویسندگان
چکیده
We provide a characterization of strictly stationary solutions to the stochastic recurrence equation zk = c(εk−1)zk−1 + g(εk−1) with Borel–measurable functions c and g, and independent, identically distributed random variables {εk}. Strictly stationary solutions that are functions of the past, respectively, of the future exist if and only if the expected value E log |c(ε0)| is negative, respectively, positive. The main result of the paper is to show that there is no solution that is a function of the past or the future if E log |c(ε0)| = 0. AMS 2000 Subject Classification: Primary 60G10, Secondary 62M10, 91B84.
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