Stochastic population processes. Analysis, approximation, simulations. (English) Zbl 1303.92001
Oxford: Oxford University Press (ISBN 978-0-19-957531-2/hbk). xii, 652 p. (2011).
Publisher’s 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:
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.
This text, strongly oriented towards problem solving, has three aims:
- 1.
- basic analytic tools are introduced through a suite of stochastic processes which do possess relatively simple closed-form solutions;
- 2.
- techniques are presented that enable the extraction of considerable behavioural information even when exact probability structures are intractable to direct solution;
- 3.
- 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.
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.
MSC:
92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |
60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |
92D25 | Population dynamics (general) |
60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |