The spine of two-particle Fleming-Viot process in a bounded interval
Krzysztof Burdzy, J\'anos Engl\"ander, Donald E. Marshall
TL;DR
This paper investigates the behavior of the spine in a two-particle Fleming-Viot process within a bounded interval, revealing it differs from a conditioned Brownian motion and providing estimates for the additional drift involved.
Contribution
It demonstrates that the spine's law in this process is distinct from the conditioned Brownian motion and quantifies the extra drift term.
Findings
The spine's law differs from Brownian motion conditioned to stay in the interval.
An estimate for the extra drift in the process is provided.
The analysis enhances understanding of the Fleming-Viot process dynamics.
Abstract
We show that the spine of the Fleming-Viot process driven by Brownian motion and starting with two particles in a bounded interval has a different law from that of Brownian motion conditioned to stay in the interval forever. Furthermore, we estimate the ``extra drift.''
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Diffusion and Search Dynamics