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Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
ISBN: 1139489739
Category : Mathematics
Languages : en
Pages : 394
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Book Description
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Author: Vassili N. Kolokoltsov
Publisher: Cambridge University Press
ISBN: 1139489739
Category : Mathematics
Languages : en
Pages : 394
Get Book Here
Book Description
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Author: V. N. Kolokol't?s?ov
Publisher:
ISBN: 9780511789489
Category : Mathematics
Languages : en
Pages : 395
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Book Description
A careful exposition of the most fundamental questions in the theory of nonlinear Markov processes.
Author: Wendell H. Fleming
Publisher: Springer Science & Business Media
ISBN: 0387310711
Category : Mathematics
Languages : en
Pages : 436
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Book Description
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Author: Vassili N. Kolokoltsov
Publisher: Walter de Gruyter
ISBN: 3110250101
Category : Mathematics
Languages : en
Pages : 449
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Book Description
This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for
Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Category : Mathematics
Languages : en
Pages : 600
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Book Description
Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.
Author: Alexandra V. Antoniouk
Publisher: Walter de Gruyter
ISBN: 3110288532
Category : Mathematics
Languages : en
Pages : 328
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Book Description
The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. The book provides also with a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. Many areas within life sciences are becoming increasingly quantitative and the progress in those areas will be more and more dependent on the successful development of advanced mathematical, statistical and modelling methodologies and techniques. The state-of-the-art developments in such methodologies and techniques are scattered throughout research journals and hardly accessible to the practitioners in those areas. This book identifies a number of frontier areas where such methodologies and techniques have recently been developed and are to be published here for the first time, bringing substantial potential benefit to a range of applications in life sciences. In addition, the book contains several state-of-the-art surveys at the interface of mathematics and life sciences that would benefit a larger interdisciplinary community. It is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.
Author: Wendell H. Fleming
Publisher: Edizioni della Normale
ISBN: 9788876422508
Category : Mathematics
Languages : en
Pages : 0
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Book Description
These notes are based on a series of lectures delivered at the Scuola Normale Superiore in March 1986. They are intended to explore some connections between the theory of control of Markov stochastic processes and certain classes of nonlinear evolution equations. These connections arise by considering the dynamic programming equation associated with a stochastic control problem. Particular attention is given to controlled Markov diffusion processes on finite dimensional Euclidean space. In that case, the dynamic programming equation is a nonlinear partial differential equation of second order elliptic or parabolic type. For deterministic control the dynamic programming equation reduces to first order. From the viewpoint of nonlinear evolution equations, the interest is in whether one can find some stochastic control problem for which the given evolution equation is the dynamic programming equation. Classical solutions to first order or degenerate second order elliptic/parabolic equations with given boundary Cauchy data do not usually exist. One must instead consider generalized solutions. Viscosity solutions methods have substantially extended the theory.
Author: Dan Crisan
Publisher: Springer Science & Business Media
ISBN: 3642153585
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume “Stochastic Analysis 2010” provides a sample of the current research in the different branches of the subject. It includes the collected works of the participants at the Stochastic Analysis section of the 7th ISAAC Congress organized at Imperial College London in July 2009.
Author: Saber Elaydi
Publisher: Springer Nature
ISBN: 303125225X
Category : Mathematics
Languages : en
Pages : 534
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Book Description
This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.
Author: Vassili N. Kolokoltsov
Publisher: Springer
ISBN: 3030123715
Category : Mathematics
Languages : en
Pages : 196
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Book Description
There has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games. Exhibiting various real world problems involving major and minor agents, this book presents a systematic continuous-space approximation approach for mean-field interacting agents models and mean-field games models. After describing Markov-chain methodology and a modeling of mean-field interacting systems, the text presents various structural conditions on the chain to yield respective socio-economic models, focusing on migration models via binary interactions. The specific applications are wide-ranging – including inspection and corruption, cyber-security, counterterrorism, coalition building and network growth, minority games, and investment policies and optimal allocation – making this book relevant to a wide audience of applied mathematicians interested in operations research, computer science, national security, economics, and finance.
