Monotone Random Systems : Theory and Applications (Lecture Notes in Mathematics)

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications. General Facts about Random Dynamical System.- Generation of Random Dynamical Systems.- Order-Preserving Random Dynamical Systems.- Sublinear Random Dynamical Systems.- Cooperative Random Differential Equations.- Cooperative Stochastic Differential Equations.