ABSTRACT
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2.1 Introduction In studying a wide variety of real-world phenomena we usually encounter pro-
cesses the course of which cannot be predicted beforehand. For example: sudden deviation of the altitude of an aircraft from a prescribed flight level; reproduction of bacteria in a favorable environment; movement of a stock price on a stock exchange. Such processes can be represented by stochastic movement of a point in a particular space specially selected for each problem. The proper choice of the phase space turns physical, mechanical, or any other real-world system into a dynamical system (it means that the current state of the system determines its future evolution). Similarly, by a proper choice of the phase space (or state space) an arbitrary stochastic process can be turned into a Markov process, i.e., a process the future evolution of which depends on the past only through its present state. This property is called the Markov property. From a whole set of stochastic processes this Markov property
singles out a class of Markov processes for which powerful mathematical tools are available.
