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8 produkter
8 produkter
Inbunden, Engelska, 1994
1 073 kr
Skickas inom 10-15 vardagar
The evolution of systems is a growing field of interest stimulated by many possible applications. This work is devoted to semi-Markov random evolutions (SMRE). This class of evolutions is rich enough to describe the evolutionary systems changing their characteristics under the influence of random factors. At the same time there exist efficient mathematical tools for investigating the SMRE. The topics addressed in this book include classification, fundamental properties of the SMRE, averaging theorems, diffusion approximation and normal deviations theorems for SMRE in ergodic case and in the scheme of asymptotic phase lumping. Both analytic and stochastic methods for investigation of the limiting behaviour of SMRE are developed. This text includes many applications of rapidly changing semi-Markov random media, including storage and traffic processes, branching and switching processes, stochastic differential equations, motions on Lie groups, and harmonic oscillations. This volume should be of interest to statisticians whose work involves operator theory, functional analysis, systems theory and cybernetics.
Inbunden, Engelska, 1997
540 kr
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This handbook on random evolutions and their applications summarizes and orders the ideas, methods, results and literature on the theory of random evolutions since 1969 and their applications to the evolutionary stochastic systems in random media. It also points out some new trends. Among the subjects treated are the problems for different models of random evolutions, multiplicative operator functionals, evolutionary stochastic systems in random media, averaging, merging, diffusion approximation, normal deviations, rates of convergence for random evolutions and their applications. The text also considers developments such as the analogue of Dynkin's formula, boundary value problems, stability and control of random evolutions, stochastic evolutionary equations, driven space-time white noise and random evolutions in financial mathematics. This handbook should be of use to theoretical and practical researchers whose interests include probability theory, functional analysis, operator theory, optimal control or statistics, and who wish to know what kind of information is available in the field of random evolutions and their applications.
Inbunden, Engelska, 2000
1 073 kr
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Covering trends in random evolution and their applications to the stochastic evolutionary system, this work contains new developments such as an analogue of Dynkin's formula, boundary value problems, stability and control of random evolutions, stochastic evolutionary equations, and driven martingale measures. In addition, it treats statistics of random evolutions processes, statistics of financial stochastic models, and stochastic stability and control of financial markets. This volume should be of interest to research and applied mathematicians working in the fields of applied probability, stochastic processes, and random evolutions, as well as experts in statistics, finance and insurance.
Inbunden, Engelska, 2003
540 kr
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The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X.Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.
Häftad, Engelska, 2010
1 073 kr
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This book is devoted to new trends in random evolution and their applications to the stochastic evolutionary system. It contains new developments such as an analogue of Dynkin's formula, boundary value problems, stability and control of random evolutions, stochastic evolutionary equations, and driven martingale measures. In addition, it treats statistics of random evolutions processes, statistics of financial stochastic models, and stochastic stability and control of financial markets. Audience: This volume will be of interest to research and applied mathematicians working in the fields of applied probability, stochastic processes, and random evolutions, as well as experts in statistics, finance and insurance.
Del 18 - Mathematical Modelling: Theory and Applications
Evolution of Biological Systems in Random Media: Limit Theorems and Stability
Häftad, Engelska, 2010
556 kr
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The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X.Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.
Häftad, Engelska, 2012
1 073 kr
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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 described by the Markov renewal processes or by the semi Markov processes. The local characteristics of the system depend on the state of the ran dom medium. At the same time, the evolution of the system does not affect the medium. Hence, the semi-Markov random evolutions are described by two processes, namely, by the switching Markov renewal process, which describes the changes of the state of the external random medium, and by the switched process, i.e., by the semigroup of oper ators describing the evolution of the system in the semi-Markov random medium.
Häftad, Engelska, 2012
540 kr
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The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.