The Kingman tree length process has infinite quadratic variation

@article{Dahmer2014TheKT,
  title={The Kingman tree length process has infinite quadratic variation},
  author={Iulia Dahmer and Robert Knobloch and A. Wakolbinger},
  journal={Electronic Communications in Probability},
  year={2014},
  volume={19},
  pages={1-12}
}
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 (cadlag) 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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