Systems in Stochastic Equilibrium presents a study of Statistical Equilibrium in systems of interacting components. The central theory of the work is the interaction known as weak coupling, which can be applied to models in both scientific and socio-economic fields. The author has included much new material on subjects such as weak coupling, partial balance and insensitivity, polymerisation, ecological competition and role- adaption in interaction models. Other topics covered include the relation of spatial processes to equilibrium concepts, reversibility and its variants, and the use of convex analysis to clarify the extremal criteria which characterise statistical equilibria.
Author(s): Peter Whittle
Series: Probability & Mathematical Statistics
Publisher: John Wiley & Sons Ltd
Year: 1986
Language: English
Pages: 470
Tags: Probability Statistics Applied Mathematics Science Math Stochastic Modeling
Contents
Preface
Part I Basic material
Equilibrium concepts; notation
2 Markov processes: standard material
3 Markov processes: supplementary material
4 Reversibility
Part II Abundance and transfer models
5 Markov models and statistical mechanics: basic
6 Markov models and statistical mechanics: variations
7 Chemical kinetics and equilibrium
8 Resource-induced ecological competition
Part III Network models
9 Jackson networks
l 0 Jackson networks with structured nodes
I I Weak coupling
12 Insensitivity
Part IV Bonding models; polymerization and random graphs
13 Polymerization; the simplest models
14 Polymer and unit statistics
15 Compartmental statistics
16 Multi-type models
17 Role-adaptation; new critical effects
Part V Spatial models; random fields
18 Random fields
19 Gaussian random fields
20 Random fields generated by dynamic models
Appendices
Stochastic invariance and equivalence
2 Hamiltonian structure
3 Constrained maximization
References
Index
