Random arithmetic-geometric means and random pi: observations and conjectures

Joel E. Cohen and Thomas M. Liggett

Stochastic Processes and their Applications, 1992, vol. 41, issue 2, 261-271

Abstract: Two random versions of the arithmetic-geometric mean of Gauss, Lagrange and Legendre are defined. Almost sure convergence and nondegeneracy are proved. These random arithmetic-geometric means in turn define two random versions of [pi]. Based on numerical simulations, inequalities and equalities are conjectured. A special case is proved. Further proofs are invited.

Keywords: nonlinear; iteration; elliptic; integrals; pi; Markov; processes; with; discrete; parameter (search for similar items in EconPapers)
Date: 1992
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