A note on invariant measures for HJM models

This note analyzes the mean-reverting behavior of time-homogeneous Heath-Jarrow-Morton (HJM) forward rate models in the weighted Sobolev spaces {H<Subscript> w </Subscript>}<Subscript> w </Subscript>. An explicit sufficient condition is given under which invariant measures exist for the HJM dynamics. In particular, every HJM model with constant volatility and market price of risk has a family of invariant measures parametrized by the distribution of the long rate. Copyright Springer-Verlag Berlin/Heidelberg 2005