The large deviations theorem and ergodicity |
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Authors: | Rongbao Gu |
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Institution: | aSchool of Finance, Nanjing University of Finance and Economics, Nanjing 210046, PR China |
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Abstract: | In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions. |
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