Fractional moments of solutions to stochastic recurrence equations
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Abstract
In this paper we study the fractional moments of the stationary solution to a stochastic recursion. We derive recursive formulas for the fractional moments of the solution. Special attention is given to the case when the additive term has an Erlang distribution. We provide various approximations to the moments and show their performance in a small numerical study
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Gennady Samorodnitsky's research was
partially supported by the ARO
grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant
H98230-11-1-0154 at Cornell University
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2012-03-13
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random recursion; fractional moment; stationary solution; GARCH
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technical report