At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten- sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat- ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop- ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong...

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten- sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat- ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop- ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong...