Abstract: Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of R. Pyke and R. Schaufele (1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example in finance and insurance. Unfortunately, no limit theorems have been ...

Most probabilistic risk assessment (PRA) and reliability methods commonly used at Johnson Space Center (JSC) make the assumption that component failures in a system are independent random occurrences. There are some exceptions (e.g. modeling common cause events), but because of the mathematical complications that occur when full dependency is assumed, it is not done by the standard models. This...

The non-Markovianity of the stochastic process called quantum semi-Markov (QSM) is studied using a recently proposed quantification memory based on deviation from semigroup evolution, that provides unified description divisible and indivisible channels. This shown to bring out property QSM processes exhibit effects even in CP-divisible regime, agreement with an earlier result. An operational me...

It is well known that in case of complex semi‐ Markov models the calculating of the exact probability distribution of the first passage time to subset of states, usually is very difficult. Then, the only way it seems to be is finding the approximate probability distribution of that random variable. It is possible by using the results from the theory of semi-Markov processes perturbations. The p...