Tails of bivariate stochastic recurrence equation with triangular matrices

We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions W=(W1,W2). Recently it has been observed that W1,W2 may exhibit regularly varying tails different indices, which is in contrast to well-known Kesten-type results. However, only partial results have derived. Under typical “Kesten–Goldie” “Grey” conditions, completely W1,W2. The asymptotics obtain not previous settings equations.