# Limit theorems for reflected Ornstein-Uhlenbeck processes

G. Huang, M.R.H. Mandjes, P.J.C. Spreij

## Samenvatting

This paper studies one-dimensional Ornstein-Uhlenbeck 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_t\$ and the `loss process' \$U_t\$, which are the minimal nondecreasing processes which make the OU process remain \$\geqslant 0\$ and \$\leqslant d\$, respectively. We derive central limit theorems for \$U_t\$ and \$L_t\$, using techniques from stochastic integration and the martingale central limit theorem.
Originele taal-2 Engels s.n. 17 Gepubliceerd - 2013

### Publicatie series

Naam arXiv.org 1304.0332 [math.PR]

## Vingerafdruk

Duik in de onderzoeksthema's van 'Limit theorems for reflected Ornstein-Uhlenbeck processes'. Samen vormen ze een unieke vingerafdruk.