Abstract
In this work we study the fractional Ornstein-Uhlenbeck bridges. First, we recall the notion of the fractional Brownian motion (fBm) and introduce a linear stochastic differential equation which is driven by (fBm) instead of standard Brownian motion.
We summarize the results on existence and uniqueness of solutions to these equations that are called the fractional Ornstein-Uhlenbeck processes. We introduce a concept of the Gaussian bridge and we derive its representation, which we use for obtaining the formula for fractional Ornstein-Uhlenbeck bridge.
The results are applied to one special example. In the last part of the paper we mention a nonanticipative representation of the bridge.