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Semi-Markov models are a generalization of Markov models that allow the time spent in a state

to be represented by an arbitrary probability distribution and the state transition probabilities to be

dependent on the time that has been spent in that state (Puterman 1994).

In a Markov model, time spent in a state can be modeled only as a self-transition, which has an exponential distribution.

One way of avoiding this limitation is to transform the semi-Markov model into an approximately equivalent fully Markov model.

For instance, Younes finds approximate solutions for generalized semi- Markov decision process models

by replacing each semi- Markov state with a phase type distribution, a series of fully Markov states that

approximate a continuous distribution, and then solving the resulting continuous-time Markov decision process (Younes & Simmons 2004).

This work has only been applied to fully observable planning problems.

However, phase type distributions have been used by Duong et.al. to approximate hidden semi-Markov

models for action recognition of everyday household activities (Duong et al. 2005).

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