V. S. Koroliuk Vladimir S. Korolyuk Anatoly F. Turbin
During the investigation of large systems described by evolution equations, we encounter many problems. Of special interest is the problem of "high dimensionality" or, more precisely, the problem of the complexity of the phase space. The notion of the "comple xity of the. phase space" includes not only the high dimensionality of, say, a system of linear equations which appear in the mathematical model of the system (in the case when the phase space of the model is finite but very large), as this is usually understood, but also the structure of the phase space itself, which can be a finite,...
During the investigation of large systems described by evolution equations, we encounter many problems. Of special interest is the problem of "high di...
V. S. Koroliuk Vladimir S. Korolyuk Yu V. Borovskich
The theory of U-statistics goes back to the fundamental work of Hoeffding 1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence...
The theory of U-statistics goes back to the fundamental work of Hoeffding 1], in which he proved the central limit theorem. During last forty years t...
Vladimir S. Korolyuk Vladimir V. Korolyuk V. S. Koroliuk
In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models...
In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematic...
The evolution of systems in random media is a broad and fruitful field for the applica tions of different mathematical methods and theories. This evolution can be character ized by a semigroup property. In the abstract form, this property is given by a semigroup of operators in a normed vector (Banach) space. In the practically boundless variety of mathematical models of the evolutionary systems, we have chosen the semi-Markov ran dom evolutions as an object of our consideration. The definition of the evolutions of this type is based on rather simple initial assumptions. The random medium is...
The evolution of systems in random media is a broad and fruitful field for the applica tions of different mathematical methods and theories. This evol...
The theory of U-statistics goes back to the fundamental work of Hoeffding 1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence...
The theory of U-statistics goes back to the fundamental work of Hoeffding 1], in which he proved the central limit theorem. During last forty years t...
During the investigation of large systems described by evolution equations, we encounter many problems. Of special interest is the problem of "high dimensionality" or, more precisely, the problem of the complexity of the phase space. The notion of the "comple- xity of the. phase space" includes not only the high dimensionality of, say, a system of linear equations which appear in the mathematical model of the system (in the case when the phase space of the model is finite but very large), as this is usually understood, but also the structure of the phase space itself, which can be a finite,...
During the investigation of large systems described by evolution equations, we encounter many problems. Of special interest is the problem of "high di...
