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Stochastic population processes : analysis, approximations, simulations

Author: Eric Renshaw
Publisher: Oxford : Oxford University Press, 2015.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
A reference text presenting stochastic processes and a range of approximation and simulation techniques for extracting behavioural information in the context of stochastic population dynamics.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Renshaw, Eric.
Stochastic population processes.
Oxford : Oxford University Press, 2015
(OCoLC)908128167
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Eric Renshaw
ISBN: 9780191060397 0191060399
OCLC Number: 1091626708
Description: 1 online resource
Contents: Cover; Contents; Preface; 1 Introduction; 1.1 Some simple stochastic processes; 1.2 Single-species population dynamics; 1.3 Bivariate populations; 1.4 Spatial-temporal processes; 2 Simple Markov population processes; 2.1 Simple Poisson process; 2.1.1 Time to subsequent events; 2.1.2 Number of events; 2.1.3 General moments; 2.1.4 Simulation; 2.1.5 Generalizations; 2.1.6 Do moments uniquely define a distribution?; 2.2 Pure death process; 2.2.1 Stochastic model; 2.2.2 Reverse transition probabilities; 2.2.3 Bridge probabilities; 2.3 Pure birth process; 2.3.1 Stochastic model 2.6 Simple immigration-emigration process2.6.1 Equilibrium distribution; 2.6.2 Time-dependent solutions; 2.7 Batch events; 2.7.1 Birth-mass annihilation and immigration process; 2.7.2 Mass immigration-death process; 2.7.3 Regenerative phenomena; 3 General Markov population processes; 3.1 Classification of states; 3.2 Equilibrium solutions; 3.2.1 Logistic population growth; 3.2.2 Simulated realizations; 3.2.3 Multiple equilibria; 3.2.4 Power-law processes; 3.3 Time-dependent solutions; 3.3.1 Approximate solutions; 3.3.2 Probability of ultimate extinction; 3.3.3 Mean time to ultimate extinction 3.4 Moment closure3.4.1 Cumulant equations; 3.5 Avoiding the Kolmogorov equations; 3.5.1 Generating cumulant equations directly; 3.5.2 Local approximations; 3.5.3 Application to Africanized honey bees; 3.6 Diffusion approximations; 3.6.1 Equilibrium probabilities; 3.6.2 Perturbation methods; 3.6.3 Additive mass-immigration process; 3.7 The saddlepoint approximation; 3.7.1 Basic derivation; 3.7.2 Examples; 3.7.3 Relationship with the Method of Steepest Descents; 3.7.4 The truncated saddlepoint approximation; 3.7.5 Final comments; 4 The random walk; 4.1 The simple unrestricted random walk 4.1.1 Normal approximation4.1.2 Laws of large numbers; 4.1.3 Using the 'reflection' principle; 4.1.4 First passage and return probabilities; 4.1.5 Probability of long leads: the First Arc Sine Law; 4.1.6 Simulated illustration; 4.2 Absorbing barriers; 4.2.1 Probability of absorption at time n; 4.2.2 One absorbing barrier; 4.2.3 Number of steps to absorption; 4.2.4 Further aspects of the unrestricted random walk; 4.3 Reflecting barriers; 4.3.1 General equilibrium probability distribution; 4.3.2 Relation between reflecting and absorbing barriers; 4.3.3 Time-dependent probability distribution
Responsibility: Eric Renshaw.

Abstract:

A reference text presenting stochastic processes and a range of approximation and simulation techniques for extracting behavioural information in the context of stochastic population dynamics.

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