Zeitschrift für Analysis und ihre Anwendungen

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Volume 30, Issue 2, 2011, pp. 237–251
DOI: 10.4171/ZAA/1433

Endogeny for the Logistic Recursive Distributional Equation

Antar Bandyopadhyay[1]

(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