Zeitschrift für Analysis und ihre Anwendungen
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Endogeny for the Logistic Recursive Distributional EquationAntar Bandyopadhyay (1) Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016, NEW DELHI, INDIA
In this article we prove the endogeny and bivariate uniqueness property for a particular “max-type” recursive distributional equation (RDE). The RDE we consider is the so called logistic RDE, which appears in the proof of the ζ(2)-limit of the random assignment problem using the local weak convergence method proved by D. Aldous [Probab. Theory Related Fields 93 (1992)(4), 507–534]. This article provides a non-trivial application of the general theory developed by D. Aldous and A. Bandyopadhyay [Ann. Appl. Probab. 15 (2005)(2), 1047–1110]. The proofs involve analytic arguments, which illustrate the need to develop more analytic tools for studying such max-type RDEs.
Keywords: Bivariate uniqueness, endogeny, logistic distribution, random assignment problem, recursive distributional equations, recursive tree processes
Bandyopadhyay Antar: Endogeny for the Logistic Recursive Distributional Equation. Z. Anal. Anwend. 30 (2011), 237-251. doi: 10.4171/ZAA/1433