Feller-continuous process
In mathematics, a Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the future depend continuously on the initial condition of the process. The concept is named after Croatian-American mathematician William Feller.
Definition
Let X : depends continuously upon x.Examples
- Every process X whose paths are almost surely constant for all time is a Feller-continuous process, since then Ex is simply g, which, by hypothesis, depends continuously upon x.
- Every Itô diffusion with Lipschitz-continuous drift and diffusion coefficients is a Feller-continuous process.