Determination of eigenvalues and eigenfunctions of a stochastic evolution operator
In the presence of white noise in a dynamical system, the delta-shaped core of
the Perron-Frobenius operator becomes a Gaussian. For a noisy one-dimensional
map or flow with a single fixed point, it is possible to find the eigenspectrum
and an invariant measure of such operator analytically. In two dimensions, a
noisy cicular limit cycle is discussed.
Content of my presentation (references are
given at the end of the report)