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Discrete Time Processes Embedded in Continuous Time Systems

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Chaos, Fractals, and Noise

Part of the book series: Applied Mathematical Sciences ((AMS,volume 97))

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Abstract

In this chapter, our goal is to introduce a way in which discrete time processes may be embedded in continuous time systems without altering the phase space. To do this, we adopt a strictly probabilistic point of view, not embedding the deterministic system S: X → X in a continuous time process, but rather embedding its Frobenius-Perron operator P:L 1 (X) →L 1 (X) that acts on L 1 functions. The result of this embedding is an abstract form of the Boltzmann equation. This chapter requires some elementary definitions from probability theory and a knowledge of Poisson processes, which are introduced following the preliminary remarks of the next section.

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© 1994 Springer Science+Business Media New York

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Lasota, A., Mackey, M.C. (1994). Discrete Time Processes Embedded in Continuous Time Systems. In: Chaos, Fractals, and Noise. Applied Mathematical Sciences, vol 97. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4286-4_8

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  • DOI: https://doi.org/10.1007/978-1-4612-4286-4_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8723-0

  • Online ISBN: 978-1-4612-4286-4

  • eBook Packages: Springer Book Archive

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