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Gaussian iterative algorithm and integrated automorphism equation for random means

  • * Corresponding author: Witold Jarczyk

    * Corresponding author: Witold Jarczyk
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  • Gauss-type iterates for random means are considered and their limit behaviour is studied. Among others the invariance of the limit with respect to the given random mean-type mapping $ {\bf{M}} $ is established under some relatively weak assumptions. The algorithm is applied to prove the existence and uniqueness of solutions $ \varphi $ of the equation

    $ \varphi({\bf x}) = \int_{\Omega}\varphi\left({\bf{M}}({\bf x},\omega)\right)dP(\omega) $

    in the class of (deterministic) means in $ p $ variables.

    Mathematics Subject Classification: Primary: 26A18, 37E05, 39B12; Secondary: 26E60, 60F17.


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