Electronic Communications in Probability

The Kingman tree length process has infinite quadratic variation

Iulia Dahmer, Robert Knobloch, and Anton Wakolbinger

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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).

Article information

Source
Electron. Commun. Probab. Volume 19 (2014), paper no. 87, 12 pp.

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

Permanent link to this document
http://projecteuclid.org/euclid.ecp/1465316789

Digital Object Identifier
doi:10.1214/ECP.v19-3318

Mathematical Reviews number (MathSciNet)
MR3298276

Zentralblatt MATH identifier
1327.60184

Subjects
Primary: 60G17: Sample path properties
Secondary: 92D25: Population dynamics (general)

Keywords
Kingman coalescent tree length process quadratic variation look-down graph

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Dahmer, Iulia; Knobloch, Robert; Wakolbinger, Anton. The Kingman tree length process has infinite quadratic variation. Electron. Commun. Probab. 19 (2014), paper no. 87, 12 pp. doi:10.1214/ECP.v19-3318. http://projecteuclid.org/euclid.ecp/1465316789.


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