Let $X_t$ be an alternating renewal process on the state space {'off', 'on'}. We can think of the process as sojourning in those states. Let $[0,\tau]$ be an interval of time and $s < \tau$.

What is the probability that during $[0,\tau]$, the process has at least one sojourn of duration less than $s$ ? (eg It flicks from 'on' to 'off' and then back to 'on' within duration $s$, at least once during the time interval.)

(I'm attempting to address an earlier question that I posed, with specialization to alternating renewal processes.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.