The Multiplicative Ergodic Theorem Of One Class Of Stochastic Dynamic Stystem

The stochastic differential equation and dynamical systems can generate a random dynamic system. This is a hot issue of research in recent years.The most basic and important of the theory of the dynamic system is to reveal the dynamics of the long-term development of the system which properties and the basic dynamic characteristics. That is the asymptotic behavior.Ergodicity is refers to the long time asymptotic behavior.The paper is arranged as follows:In the first chapter, this paper firstly describes the background and main results. Then we present in this paper, involving the basic concepts and notation, and introduce some random process theory and basic concept in the theory of stochastic dynamic system, including the Ito’s formula and ergodic theorem.In the second chapter, we give a special kind of oscillator, the oscillator is composed of n chain, the chain dynamics system can be used to describe the Hamilton function.Both ends of the oscillator chain are respectively connected with the heat bath. The interaction between heat bath and chain through differential equations (often referred to as the system) to describe.After a series of derivation, the main use of Ito’s formula, get the multiplicative ergodic theorem of the corrsponding stochastic dynamic system.In the third chapter, the first section gives a multiplicative ergodic model needs to meet the condi-tions. The second section according to the conditions of the first section lists the six special model. And illustrates them respectively with multiplicative ergodic theorem.