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2014 The Kingman tree length process has infinite quadratic variation
Iulia Dahmer, Robert Knobloch, Anton Wakolbinger
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-3318

Abstract

In the case of neutral populations of fixed sizes in equilibrium whose genealogies are described by the Kingman N-coalescent back from time t consider the associated processes of total tree length as t increases. We show that the (càdlàg) process to which the sequence of compensated tree length processes converges as N tends to infinity is a process of infinite quadratic variation; therefore this process cannot be a semimartingale. This answers a question posed in Pfaffelhuber et al. (2011).

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Iulia Dahmer. Robert Knobloch. Anton Wakolbinger. "The Kingman tree length process has infinite quadratic variation." Electron. Commun. Probab. 19 1 - 12, 2014. https://doi.org/10.1214/ECP.v19-3318

Information

Accepted: 20 December 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60184
MathSciNet: MR3298276
Digital Object Identifier: 10.1214/ECP.v19-3318

Subjects:
Primary: 60G17
Secondary: 92D25

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