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sahildh
Member
Why do the kolmogorov equations for time inhomogeneous markov chains take into consideration the time spent (waiting time) in a state whereas this is not so in case of time homogeneous markov chains ???
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Hemant Rupani
Senior Member
Because, in time homogeneous Markovian, rate is independent of time...'
if it depends, it'll be time-inhomogeneous...
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sahildh
Member
Ok ! So we can say that only in time inhomogeneous Markov process the kolmogorov equations take into account the probability of waiting in a state.
Well, can u tell me then why is this so ? I mean why is the probability of transition affected by the probability of waiting in a particular state even though we are taking into account the time inhomogenity in its transition rate?
Well, can u tell me then why is this so ? I mean why is the probability of transition affected by the probability of waiting in a particular state even though we are taking into account the time inhomogenity in its transition rate?
Hemant Rupani
Senior Member
Yes, affect of waiting time to transitions can be present in time-inhomogeneous case only.
suppose, a persons in sick for a year and (s)he has transition rate of \(\mu \) to death... but after 2-3 more years of sickness, transition rate to the death would be more... in other words, here transition rate increase(time inhomogenous) with time spent in Sick State