Chaos and Stochastic Systems

  • Kung-Sik Chan
  • Howell Tong
Part of the Springer Series in Statistics book series (SSS)


As we have seen in Chapter 2, a deterministic dynamical system describes the transition from the initial state to the later states, where the transition law, i.e. the dynamics, is assumed to be known precisely and the states are assumed to be free from any errors, such as measurement errors, rounding errors, etc. In reality, such assumptions are rarely satisfied. We should therefore extend the deterministic dynamical system to a stochastic dynamical system, which treats the states as random and describes the transition probabilities from the initial state to the later states. A natural way of characterising the ‘driving force’ behind a stochastic dynamical system is to introduce dynamic noise, also known as system noise.


Markov Chain Lyapunov Exponent Invariant Measure Stochastic System Invariant Probability Measure 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Kung-Sik Chan
    • 1
  • Howell Tong
    • 2
    • 3
  1. 1.Department of Statistics and Actuarial ScienceThe University of IowaIowa CityUSA
  2. 2.Department of StatisticsThe London School of Economics and Political ScienceLondonUK
  3. 3.The University of Hong KongHong Kong

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