Generalized Semi-Markov Process models (GSMP) |
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DescriptionDefinitionExamplesReferences |
Description:
Here we follow the definition of GSMP model given in [1]. GSMP is a stochastic process in which a transition from one state to another is triggered by one or more events.
Note that not all definitions of GSMP available in the literature coincide with this. For example some definitions of GSMP do not allow for multiple events occurring simultaneously. We treat this as a separate formalism – GSMP without simultaneous events. Formal
Definition:
A Generalized Semi-Markov Process (GSMP) model has the following components: E – is a finite set of events X – is a countable set of states Γ(x) – is a set of active events defined for all x ∈X,
with Γ(x) a subset of E, p(x1; x, E*) – is a state transition probability,
defined for all x, x1 ∈X, E*a subset of E, reflecting
probability of going from state x to state x1 through simultaneous
occurrence of events in E*. p0(x)
– is the pmf P[X0=x], x∈X, of
the initial state X0. G={Gi : i∈E}
– is a stochastic clock structure – a set of distribution functions. Note1: Another feature may be (and
usually is) incorporated in this formalism – clock rates that in general depend on states. We are not
considering this feature for now. Examples:
References:
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