Resumen de Fractional moments of solutions to stochastic recurrence equations
Thomas Mikosch,, Gennady Samorodnitsky, Laleh Tafakori
In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = At Xt- 1 + Bt, t ? Z, where ((At, Bt)) t ? Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments ?|X0|p, p ? R. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments ?|X0lp and show their performance in a small numerical study.
