Fractional moments of  solutions to stochastic recurrence equations

Thomas Valentin Mikosch; Muneya  Matsui; Laleh  Tafakori

Fractional moments of solutions to stochastic recurrence equations

Thomas Valentin Mikosch, Muneya Matsui, Laleh Tafakori

Department of Mathematical Sciences

8 Citations (Scopus)

Abstract

In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation X_t = A_tX_t-1 + B_t, t ∈ ℤ, where ((A_t, Bt)) _t∈ℤ is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X ₀|^p, p∈ℝ. Special attention is given to the case when B_t has an Erlang distribution. We provide various approximations to the moments E|X₀|^p and show their performance in a small numerical study.

Original language	English
Journal	Journal of Applied Probability
Volume	50
Pages (from-to)	969-982
ISSN	0021-9002
Publication status	Published - Dec 2013

Cite this

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title = "Fractional moments of solutions to stochastic recurrence equations",

abstract = "In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt-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 E|X 0|p, p∈ℝ. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.",

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T1 - Fractional moments of solutions to stochastic recurrence equations

AU - Mikosch, Thomas Valentin

AU - Matsui, Muneya

AU - Tafakori, Laleh

PY - 2013/12

Y1 - 2013/12

N2 - In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt-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 E|X 0|p, p∈ℝ. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.

AB - In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt-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 E|X 0|p, p∈ℝ. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.

M3 - Journal article

SN - 0021-9002

VL - 50

SP - 969

EP - 982

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -

Fractional moments of solutions to stochastic recurrence equations

Abstract

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