Basics of Stochastic Processes -- Markov Chains -- Long-run Behaviour of Markov Chains -- Random Walks -- Bienayme Galton Watson Branching Process -- Continuous Time Markov Chains -- Poisson Process -- Birth and Death Processes -- Brownian Motion Process -- Renewal Process -- Solutions...

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter...

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter...

We propose an infinitesimal dispersion index for Markov counting processes. We show that, under standard moment existence conditions, a process is infinitesimally (over-) equi-dispersed if, and only if, it is simple (compound), i.e. it increases in jumps of one (or more) unit(s), even though...

Metro station corridor width design considering demand fluctuation as well as the randomness and state-dependence of service time is an urgent concern and a complicated random planning issue. This paper confirms the accuracy of phase-type distribution (PH) fitting for passenger arrival intervals...