Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 87, 12 pp.
The Kingman tree length process has infinite quadratic variation
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).
Electron. Commun. Probab. Volume 19 (2014), paper no. 87, 12 pp.
Accepted: 20 December 2014
First available in Project Euclid: 7 June 2016
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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. https://projecteuclid.org/euclid.ecp/1465316789.