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One-Dimensional Infinite Memory Imitation Models with Noise

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Abstract

In this paper we study stochastic process indexed by \(\mathbb {Z}\) constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J Stat Phys 150(6):1017–1029, 2013).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma La Sapienza, Rome, Italy

    Emilio De Santis & Mauro Piccioni

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  1. Emilio De Santis
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  2. Mauro Piccioni
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Correspondence to Emilio De Santis.

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De Santis, E., Piccioni, M. One-Dimensional Infinite Memory Imitation Models with Noise. J Stat Phys 161, 346–364 (2015). https://doi.org/10.1007/s10955-015-1335-5

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  • DOI: https://doi.org/10.1007/s10955-015-1335-5

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