General probabilistic approach to the problem of irreversible stochastic transitions

The consideration of irreversible stochastic transitions (IST) in complex stochastic systems based on the most general probabilistic formalism is performed. The key quality, transition probability per unit time, alpha , is strictly introduced without referring to the conventional approach to the IST description. The expressions obtained for transition probabilities and average transition expectation time, ( tau ), allow one to take into account the influence of interactions between objects undergoing IST and external impacts on probabilities of transitions. The violation of common postulates alpha =1/( tau )=constant, as well as of the simple exponential kinetic law for A to B transitions is demonstrated. These postulates are shown to follow from the general consideration performed as a special particular case. The evaluation of statistical characteristics of various complex systems containing objects undergoing IST by means of the approach developed is demonstrated on two model problems.