Inference for the Wiener Process With Random Initiation Time

When considering a degradation model, it is mainly assumed that the degradation begins as soon as the device is put into service. However, in practice, sometimes the degradation occurs only after a certain delay called the initiation time (or latency period). In this paper, we consider the Wiener process, as a degradation model, starting at a random time. Such a process can also be called a randomly delayed Wiener process. Sample paths are assumed to be observed at the same regular instants. The statistical inference under this sampling scheme is studied here, providing some asymptotic results.