Absorption and stationary times for the Λ\Lambda-Wright-Fisher process

Abstract

We derive stationary and fixation times for the multi-type Λ\Lambda-Wright-Fisher process with and without the classic linear drift that models mutations. Our method relies on a grand coupling of the process realized through the so-called lookdown-construction. A well-known process embedded in this construction is the fixation line. We generalise the process to our setup and make use of the associated explosion times to obtain a representation of the fixation and stationary times in terms of the waiting time in a coupon collector problem

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