Background
Swishchuk, Anatoly Vitalievich was born on April 26, 1957 in Khmelnitskaya Region, Ukraine. Son of Vitaliy Emelianovich and Maria Alexandrovna Swishchuk.
( This is a new book in biomathematics, which includes ne...)
This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach.
http://www.amazon.com/gp/product/1402015542/?tag=2022091-20
(Evolution of Systems in Random Media is an innovative, ap...)
Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.
http://www.amazon.com/gp/product/0849394058/?tag=2022091-20
(The book is devoted to the new trends in random evolution...)
The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.
http://www.amazon.com/gp/product/0792362640/?tag=2022091-20
(The main purpose of this handbook is to summarize and to ...)
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.
http://www.amazon.com/gp/product/0792345339/?tag=2022091-20
(The evolution of systems in random media is a broad and f...)
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.
http://www.amazon.com/gp/product/9401044392/?tag=2022091-20
(The book is devoted to the new trends in random evolution...)
The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.
http://www.amazon.com/gp/product/9048154413/?tag=2022091-20
Swishchuk, Anatoly Vitalievich was born on April 26, 1957 in Khmelnitskaya Region, Ukraine. Son of Vitaliy Emelianovich and Maria Alexandrovna Swishchuk.
Master of Science, Kiev (Ukraine) State University, 1979. Candidate of Sciences, Institute of Mathematics, Kiev, 1985. Doctor of Science, Institute of Mathematics, Kiev, 1992.
Deputy science manager International Mathematics Center, Kiev, 1992-1996, head mathematics projects department, since 1996. Leading science collaborator Institute of Mathematics, 1993-1999. Lecturer Kiev State University, 1995-1998, professor, since 1998.
(The main purpose of this handbook is to summarize and to ...)
(Evolution of Systems in Random Media is an innovative, ap...)
( This is a new book in biomathematics, which includes ne...)
(The evolution of systems in random media is a broad and f...)
(The book is devoted to the new trends in random evolution...)
(The book is devoted to the new trends in random evolution...)
Senior lieutenant Ministry of Defense, Union of the Soviet Socialist Republics, 1979-1981. Member American Mathematics Society, Institute of Mathematics Statistics, Statistical Society of Canada.
Married Maria Yaroslavovna Ben, September 15, 1983. Children: Victor, Julia.