The Kingman tree length process has infinite quadratic variation
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).
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- arXiv:
- arXiv:1402.2113
- Bibcode:
- 2014arXiv1402.2113D
- Keywords:
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- Mathematics - Probability;
- 60G17;
- 92D25
- E-Print:
- 13 pages, 3 figures