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$begingroup$

Say I have a continuous time Markov chain on some state space $S$ with generator matrix $Q$, and I'm interested in the first passage time $T$ from some initial state $s_0 in S$ to some absorbing set of states $A in S$. Is it possible to rescale $Q$ (i.e. change the time scale of the Markov chain) in a way that gives a result like "$mathbbP(T leq t)$ if and only if $mathbbP(T' leq t')$", with $T'$ being the first passage time from $s_0$ to $A$ in the rescaled Markov chain with generator $Q'$?

probability markov-chains

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asked Mar 29 at 21:02

user65561user65561

1

$endgroup$

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  $begingroup$
  Say $Q$ is measured in units of "transitions per minute". You can simply change it to "transitions per hour", right? Then $T$ is measured in minutes while $T'$ is measured in hours.
  $endgroup$
  – antkam
  Mar 29 at 22:24
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Say I have a continuous time Markov chain on some state space $S$ with generator matrix $Q$, and I'm interested in the first passage time $T$ from some initial state $s_0 in S$ to some absorbing set of states $A in S$. Is it possible to rescale $Q$ (i.e. change the time scale of the Markov chain) in a way that gives a result like "$mathbbP(T leq t)$ if and only if $mathbbP(T' leq t')$", with $T'$ being the first passage time from $s_0$ to $A$ in the rescaled Markov chain with generator $Q'$?

probability markov-chains

share|cite|improve this question

asked Mar 29 at 21:02

user65561user65561

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Say $Q$ is measured in units of "transitions per minute". You can simply change it to "transitions per hour", right? Then $T$ is measured in minutes while $T'$ is measured in hours.
  $endgroup$
  – antkam
  Mar 29 at 22:24
  
  

  
  
  
  

add a comment | 

$begingroup$

Say I have a continuous time Markov chain on some state space $S$ with generator matrix $Q$, and I'm interested in the first passage time $T$ from some initial state $s_0 in S$ to some absorbing set of states $A in S$. Is it possible to rescale $Q$ (i.e. change the time scale of the Markov chain) in a way that gives a result like "$mathbbP(T leq t)$ if and only if $mathbbP(T' leq t')$", with $T'$ being the first passage time from $s_0$ to $A$ in the rescaled Markov chain with generator $Q'$?

probability markov-chains

share|cite|improve this question

asked Mar 29 at 21:02

user65561user65561

1

$endgroup$

share|cite|improve this question

asked Mar 29 at 21:02

user65561user65561

1

share|cite|improve this question

asked Mar 29 at 21:02

user65561user65561

1

asked Mar 29 at 21:02

user65561user65561

1

asked Mar 29 at 21:02

user65561user65561

1