Approximation of Population Processes PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Approximation of Population Processes PDF full book. Access full book title Approximation of Population Processes by Thomas G. Kurtz. Download full books in PDF and EPUB format.
Author: Thomas G. Kurtz
Publisher: SIAM
ISBN: 089871169X
Category : Mathematics
Languages : en
Pages : 76
Get Book
Book Description
This monograph considers approximations that are possible when the number of particles in population processes is large
Author: Thomas G. Kurtz
Publisher: SIAM
ISBN: 089871169X
Category : Mathematics
Languages : en
Pages : 76
Get Book
Book Description
This monograph considers approximations that are possible when the number of particles in population processes is large
Author: Eric Renshaw
Publisher: Oxford University Press
ISBN: 0198739060
Category : Mathematics
Languages : en
Pages : 665
Get Book
Book Description
The vast majority of random processes in the real world have no memory - the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation procedures. Traditional books, heavy in mathematical theory, often ignore such methods and attempt to force problems into a rigid framework of closed-form solutions. This text, strongly oriented towards problem solving, has three aims. First, basic analytic tools are introduced through a suite of stochastic processes which do possess relatively simple closed-form solutions. Second, techniques are presented that enable the extraction of considerable behavioral information even when exact probability structures are intractable to direct solution. Third, a range of simulation procedures is proposed which provide insight into the way that particular systems develop - these often expose hitherto unforeseen features and thereby suggest further lines of exploration. Although the examples are slanted towards ecological and physical applications, only a little imagination is required in order to apply the techniques to problems generic to engineering, chemistry and finance. Indeed, the book provides a rich source of ideas for anyone working with random processes who is prepared to take a flexible approach. Many aspects of population dynamics are covered, including: general birth-death and power-law processes; random and correlated walks; Markov chains; perturbation and saddlepoint techniques; Wiener, Fokker-Planck and Ornstein-Uhlenbeck diffusion processes; general bivariate processes, including predator-prey, competition, epidemic, cumulative size and counting systems; MCMC and simulation techniques; and velocities, dynamic structure, Turing ring systems and cellular automata for spatial-temporal systems. Extensions include fractal structure from power-law contact distributions, and marked point processes. Since little of the material is covered at a deep mathematical level, the book will be readily accessible to a wide range of researchers and practitioners, and provides an excellent basis for constructing novel undergraduate and postgraduate courses in applied probability. The unified approach exposes the high degree of linkage that exists between apparently unconnected processes. The book can also be treated as a toolbox to be dipped into in order to select specific analytic and computational techniques.
Author: Samuel Preston
Publisher: Wiley-Blackwell
ISBN: 9781557864512
Category : History
Languages : en
Pages : 308
Get Book
Book Description
This book presents and develops the basic methods and models that are used by demographers to study the behaviour of human populations. The procedures are clearly and concisely developed from first principles and extensive applications are presented.
Author: Vikram Krishnamurthy
Publisher: Cambridge University Press
ISBN: 1107134609
Category : Mathematics
Languages : en
Pages : 491
Get Book
Book Description
This book covers formulation, algorithms, and structural results of partially observed Markov decision processes, whilst linking theory to real-world applications in controlled sensing. Computations are kept to a minimum, enabling students and researchers in engineering, operations research, and economics to understand the methods and determine the structure of their optimal solution.
Author: Amarjit Budhiraja
Publisher: Springer
ISBN: 1493995790
Category : Mathematics
Languages : en
Pages : 574
Get Book
Book Description
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author: Miklos Csorgo
Publisher: SIAM
ISBN: 9781611970289
Category : Distribution (Probability theory)
Languages : en
Pages : 169
Get Book
Book Description
Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.
Author: Henry C. Tuckwell
Publisher: SIAM
ISBN: 0898712327
Category : Technology & Engineering
Languages : en
Pages : 128
Get Book
Book Description
This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.
Author: Patsy Haccou
Publisher: Cambridge University Press
ISBN: 9780521832205
Category : Mathematics
Languages : en
Pages : 342
Get Book
Book Description
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Author: Harold Joseph Kushner
Publisher: MIT Press
ISBN: 9780262110907
Category : Computers
Languages : en
Pages : 296
Get Book
Book Description
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and methods for random processes and applies them to numerous problems of practical importance. In particular, it develops usable and broad conditions and techniques for showing that a sequence of processes converges to a Markov diffusion or jump process. This is useful when the natural physical model is quite complex, in which case a simpler approximation la diffusion process, for example) is usually made. The book simplifies and extends some important older methods and develops some powerful new ones applicable to a wide variety of limit and approximation problems. The theory of weak convergence of probability measures is introduced along with general and usable methods (for example, perturbed test function, martingale, and direct averaging) for proving tightness and weak convergence. Kushner's study begins with a systematic development of the method. It then treats dynamical system models that have state-dependent noise or nonsmooth dynamics. Perturbed Liapunov function methods are developed for stability studies of nonMarkovian problems and for the study of asymptotic distributions of non-Markovian systems. Three chapters are devoted to applications in control and communication theory (for example, phase-locked loops and adoptive filters). Smallnoise problems and an introduction to the theory of large deviations and applications conclude the book. Harold J. Kushner is Professor of Applied Mathematics and Engineering at Brown University and is one of the leading researchers in the area of stochastic processes concerned with analysis and synthesis in control and communications theory. This book is the sixth in The MIT Press Series in Signal Processing, Optimization, and Control, edited by Alan S. Willsky.
Author: Paul Waltman
Publisher: SIAM
ISBN: 0898711886
Category : Technology & Engineering
Languages : en
Pages : 81
Get Book
Book Description
This book uses fundamental ideas in dynamical systems to answer questions of a biologic nature, in particular, questions about the behavior of populations given a relatively few hypotheses about the nature of their growth and interaction. The principal subject treated is that of coexistence under certain parameter ranges, while asymptotic methods are used to show competitive exclusion in other parameter ranges. Finally, some problems in genetics are posed and analyzed as problems in nonlinear ordinary differential equations.
