Spectral Decomposition of Transition Matrix
Abstract: The transition
probabilities of a two-state Markov process
can be determined explicitly. The modeling of force transition of two state Markov process using
double decrement approach is well developed in the literature. However, the
approaches are mainly analytic or illustrative and are based on small data set.
The study based on large data set are rarely published. For higher number of
states, the computation of transition probabilities is laborious, and an alternative
method is needed. This work aims to propose a spectral approach of forces of
transition that attempts to address the
issues. The method is based on results that are available when a Markov process
with constant forces of transition is assumed. In this case, transition
probabilities are obtained regardless of the number of states. A differential equation
is used to express the relationship between frces of decrements and transition
probabilities, and by assuming constant force, the explicit solution is reduced
to spectral decomposition of force of decrements. The results are the visualization
of transition probabilities, and a contribution for the development of double
decrement table. The main contributions
of this work are a spectral representation of transition probabilities and a
multistate approach to double decrement modeling.
Author: Sutawanir, Darwis
and Kuslan
Journal Code: jpmatematikagg080001
