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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