vom Scheidt, J.; Starkloff, H.-J.; Wunderlich, R. : Stationary solutions of random differential equations with polynomial nonlinearities

Author(s) :

vom Scheidt, J.; Starkloff, H.-J.; Wunderlich, R.

Title :

Stationary solutions of random differential equations with polynomial nonlinearities

Electronic source :

[gzipped dvi-file] 26 kB
[gzipped ps-file] 89 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-2, 1999

Mathematics Subject Classification :

60H10 [ Stochastic ordinary differential equations ]

34F05 [ ODE with randomness ]

70L05 [ Random vibrations (general mechanics) ]

11B83 [ Special sequences of integers and polynomials ]

Abstract :

The paper deals with systems of ODEs containing polynomial nonlinearities and random inhomogeneous terms. Applying perturbation method pathwise solutions are found in form of power series with respect to a parameter eta controlling the nonlinearities. Under the assumption that for eta=0 the system is stable and that the inhomogeneous terms are bounded the radius of convergence of the perturbation series is estimated. Further, it is proved that the perturbation series form stationary solutions if the inhomogeneous terms are stationary.

Keywords :

nonlinear differential equations, perturbation series, Catalan number, stationary solution

Language :

english

Publication time :

4/1999