Normal forms for random diffeomorphisms
The stochastic normal forms theory is developed to make random diffeomorphism as simple as possible by means of a nonlinear random coordinate transform. Stochastic versions of Lyapunov exponents and eigenspaces are introduced using Oseledec multiplicative ergodic theorem. The stochastic analogues of resonance and average are studied. No assumptions about the smallness of random perturbations are made. The unified approach presented here covers the case of stochastic differential equations as well as random difference equations. The equation eliminating nonlinear terms is infinite-dimensional.
scientific article; zbMATH DE number 94579
scientific article