A new model for realistic random perturbations of stochastic oscillators
The local boundedness of trajectories of a dissipative oscillator subject to random perturbations is proved. By using three different stochastic Poincaré maps the global boundedness of solutions is obtained. Also one proves that the probability density functions of the stochastic oscillator can be given by a rational function depending on solutions of a pair of diffusive partial differential equations with vanishing boundary conditions on finite intervals.
scientific article; zbMATH DE number 6586393
scientific article