Article ID: | iaor201522334 |
Volume: | 68 |
Issue: | 1 |
Start Page Number: | 25 |
End Page Number: | 42 |
Publication Date: | Feb 2014 |
Journal: | Statistica Neerlandica |
Authors: | Mandjes Michel, Huang Gang, Spreij Peter |
Keywords: | limit theorems |
This paper studies one‐dimensional Ornstein–Uhlenbeck (OU) processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d > 0). In the literature, they are referred to as reflected OU (ROU) and doubly reflected OU (DROU), respectively. For both cases, we explicitly determine the decay rates of the (transient) probability to reach a given extreme level. The methodology relies on sample‐path large deviations, so that we also identify the associated most likely paths. For DROU, we also consider the ‘idleness process’ L