A GENERALIZED MEAN-REVERTING EQUATION AND APPLICATIONS

作者：Marie Nicolas^*

来源：ESAIM: Probability and Statistics , 2014, 18: 799-828.

DOI：10.1051/ps/2014002

• Stochastic differential equations
• rough paths
• large deviation principle
• mean-reversion
• Gaussian processes

Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Holder continuous paths on [ 0, T] (T > 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the associated Ito map, and we provide an L-p-converging approximation with a rate of convergence (p >= 1). The regularity of the Ito map ensures a large deviation principle, and the existence of a density with respect to Lebesgue's measure, for the solution of that generalized mean-reverting equation. Finally, we study a generalized mean-reverting pharmacokinetic model.

• 出版日期2014-1