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Classification and Lumpability in the Stochastic Hopfield Model

R. L. Paige
Advances in Applied Probability
Vol. 33, No. 4 (Dec., 2001), pp. 930-943
Stable URL: http://www.jstor.org/stable/1428313
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Classification and Lumpability in the Stochastic Hopfield Model
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Abstract

Connections between classification and lumpability in the stochastic Hopfield model (SHM) are explored and developed. A simplification of the SHM's complexity based upon its inherent lumpability is derived. Contributions resulting from this reduction in complexity include: (i) computationally feasible classification time computations; (ii) a development of techniques for enumerating the stationary distribution of the SHM's energy function; and (iii) a characterization of the set of possible absorbing states of the Markov chain associated with the zero temperature SHM.

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