Some aspects of stochastic modelling
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This thesis is mainly concerned with methods for the comparison of distribution functions which depend on the whole of the distribution functions, as against those methods which depend on the comparison of derived statistics. The main methods considered are partial and preorderings (Chapter 2) and probability metrics (Chapter 4). Chapter 0 contains a general discussion of mathematical and stochastic modelling. The aim of this chapter is to introduce the concept of the structure of a...[Show more]
dc.contributor.author  Taylor, James Mackenzie  

dc.date.accessioned  20171106T01:24:21Z  
dc.date.available  20171106T01:24:21Z  
dc.date.copyright  1984  
dc.identifier.other  b1063306  
dc.identifier.uri  http://hdl.handle.net/1885/133195  
dc.description.abstract  This thesis is mainly concerned with methods for the comparison of distribution functions which depend on the whole of the distribution functions, as against those methods which depend on the comparison of derived statistics. The main methods considered are partial and preorderings (Chapter 2) and probability metrics (Chapter 4). Chapter 0 contains a general discussion of mathematical and stochastic modelling. The aim of this chapter is to introduce the concept of the structure of a stochastic model, which is fundamental to the notion of comparability of stochastic models. Chapter 1 is introductory. Chapter 2 considers the comparison of distribution functions via partial orderings. Various partial and preorderings are described and their properties studied. In particular, a survey of comparisons for certain common distribution functions is given. In Chapter 3 it is shown how the orderings introduced in Chapter 2 lead to definitions of monotonicity and comparability for stochastic models. Examples are given for Markov chains, martingales, renewal processes and queueing processes. Proofs of results of Daley (1968), Kalmykov (1962) and others on the monotonicity of Markov chains are shown to be elementary. Chapter 4 deals with the use of metrics to compare distribution functions. Some of the more common probability metrics are listed. New bounds on the supremum (uniform) metric are derived for nonnegative integervalued random variables. Probability metrics are fundamental to the notion of the stability of stochastic models, and this is considered in Chapter 5. In Chapter 6 monotonicity properties are used to investigate the behaviour of a class of branching processes which allow for interaction between male and female in the production of offspring. Sufficient conditions for certain extinction and noncertain extinction are given for the general model, whilst for models with superadditive mating functions necessary and sufficient conditions are given for almost sure extinction. Comparison of models which allow for sexual reproduction with ordinary GaltonWatson branching processes shows that, at least for small populations, there is a significant difference in both the probabilities of extinction and the rates of growth. These are investigated numerically using a truncation technique. Theoretical bounds are given for the error in the calculated values of the extinction probabilities.  
dc.format.extent  v, [ii], 214 leaves  
dc.language.iso  en  
dc.subject.lcsh  Distribution (Probability theory)  
dc.subject.lcsh  Stochastic systems  
dc.subject.lcsh  Markov processes  
dc.title  Some aspects of stochastic modelling  
dc.type  Thesis (PhD)  
local.contributor.supervisor  Daley, D.J.  
dcterms.valid  1984  
local.description.notes  Thesis (Ph.D.)Australian National University, 1984. This thesis has been made available through exception 200AB to the Copyright Act.  
local.type.degree  Doctor of Philosophy (PhD)  
dc.date.issued  1984  
local.contributor.affiliation  Department of Statistics, Research School of Social Sciences, The Australian National University  
local.identifier.doi  10.25911/5d723b9473a6f  
dc.date.updated  20171020T04:19:15Z  
local.mintdoi  mint  
Collections  Open Access Theses 
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