Chaos and Stochastic Systems
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.
KeywordsMarkov Chain Lyapunov Exponent Invariant Measure Stochastic System Invariant Probability Measure
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