Fractional moments of solutions to stochastic recurrence equations

• Autores: Thomas Mikosch,, Gennady Samorodnitsky, Laleh Tafakori
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 4, 2013, págs. 969-982
• Idioma: inglés
• DOI: 10.1239/jap/1389370094
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• Resumen

  • 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.