Large time and small noise asymptotic results for mean reverting diffusion processes with applications
The authors study certain classes of mean-reverting diffusions with constant or, respectively, state dependent noise terms. Using the theory of large deviations, the large time behaviour as well as the small noise asymptotics for both types of diffusions are investigated. In particular, the paper presents results concerning the speed with which convergence to fundamental value takes place as noise reduces to zero. Interesting examples where the asymptotic results obtained here are of relevance include certain classes of interest rate models that exhibit mean reversion; see, e.g., \textit{O. A. Vasicek} [J. Financial Econ. 5, 177-188 (1977)] and \textit{J. C. Cox}, \textit{J. E. Ingersoll jun.} and \textit{S. A. Ross} [Econometrica 53, 363-384 (1985; Zbl 0576.90006)].
scientific article; zbMATH DE number 1525344