The stochastic properties of the sojourn times attached to a Markov process in continuous time and with a finite number of states are described by using a statistical ensemble approach. This approach is applied for investigating the large time behavior of independent rate processes with...

A general approach is introduced for describing the time evolution of a Markov process in continuous time and with a finite number of states. The total number of transition events from one state to other states and of the total sojourn times of the system in the different states are used as...

A general method for constructing self-similar scalar fractal random fields is suggested based on the assumption that the fields are generated by a broad distribution of punctual sources. The method is illustrated by a problem of population biology, the evolution on a random fitness landscape. A...

A statistical-mechanical model for the propagation of a space-dependent epidemic is suggested based on the following assumptions. (1) The population is made up of three types of individuals, susceptibles, infectives and recovered. The total population size is constant and confined in a given...

The possible occurrence of ergodic behavior for large times is investigated in the case of stationary random processes with memory. It is shown that for finite times the time average of a state function is generally a random variable and thus two types of cumulants can be introduced: for the...

Three models for the fractal time statistics of renewal processes are suggested. The first two models are related to the industrial replacement. A model assumes that the state of an industrial aggregate is described by a continuous positive variable X, which is a measure of its complexity. The...

The large time behavior of stochastic cellular automata is investigated by means of an analogy with Van Kampen's approach to the ergodic behavior of Markov processes in continuous time and with a discrete state space. A stochastic cellular automaton with a finite number of cells may display an...

The influence of long memory on anomalous diffusion processes is analyzed. We assume that between two successive jumps the moving particle oscillates around an equilibrium position. The number m of oscillations between two jumps is a non-Markovian random variable with infinite memory. The system...

The multiple hierarchical fractal aggregation is used as an illustration for a new type of asymptotic behavior of fractal random processes defined in terms of a multiple Shlesinger- Hughes renormalization procedure. The joint probability distributions of aggregate sizes for a multiple...

Complex physical systems are considered, involving both random and deterministic phenomena. We introduce a set of age-dependent transition rates accounting for the random jump processes and a set of deterministic equations describing the evolution of the system between two jumps. The age-state...