Hi,
I have a general question.
Suppose that you have a two state markov chain S (suppose the states are 0 and 1). The transition probability of it, over an infinitesimal interval dt is:
\(\left[\begin{array}{cc}1-\lambda_{H}dt & \lambda_{H}dt\\\lambda_{L}dt & 1-\lambda_{L}dt\end{array}\right]\)
In other words,
\(Pr(S_{t+dt}=1|S_{t}=0)=\lambda_{H}dt\)
and
\(Pr(S_{t+dt}=0|S_{t}=1)=\lambda_{L}dt\)
I want to compute:
\(Pr(S_{t+\tau}=0|S_{t}=1)\) for some interval \(\tau>0\).
Can I compute this expression in closed form? if so, how?
Thanks
Dan
I have a general question.
Suppose that you have a two state markov chain S (suppose the states are 0 and 1). The transition probability of it, over an infinitesimal interval dt is:
\(\left[\begin{array}{cc}1-\lambda_{H}dt & \lambda_{H}dt\\\lambda_{L}dt & 1-\lambda_{L}dt\end{array}\right]\)
In other words,
\(Pr(S_{t+dt}=1|S_{t}=0)=\lambda_{H}dt\)
and
\(Pr(S_{t+dt}=0|S_{t}=1)=\lambda_{L}dt\)
I want to compute:
\(Pr(S_{t+\tau}=0|S_{t}=1)\) for some interval \(\tau>0\).
Can I compute this expression in closed form? if so, how?
Thanks
Dan
