Statistical Inference for Stochastic Processes
The aim of this monograph is to attempt to reduce the gap between theory and applications in the area of stochastic modelling, by directing the interest of future researchers to the inference aspects of stochastic processes. This is a research monograph written for specialists in the common area of stochastic processes and theoretical statistics. The topics in the book have been divided into three parts. Part I presents an introduction and discusses some standard models. In this part, main ideas and methods are emphasized, avoiding technicalities as far as possible. Part II consists of three chapters on the theory of inference for general processes in discrete and continuous time including diffusion processes. Part III surveys in three chapters recent results on Bayesian, non-parametric and sequential procedures. The treatment of the subject in Parts II and III is more rigorous than that in Part I, and the theory is emphasized here rather than the methods.
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Introductory Examples of Stochastic Models Example 1 A Random Walk Model for Neuron Firing
Chain Binomial Models in Epidemiology
A Population Growth Model
27 other sections not shown
alternative application assume assumptions asymptotically normal Bayes called Chapter Consider consistent constant continuous convergence corresponding defined Definition denote density dependent derivative diffusion process discrete discussed distribution efficient Example exists exponential finite fixed follows function Further given gives Hence holds hypothesis identically distributed implies independent inference integral interval known Lemma likelihood equation likelihood function limit linear Markov chain Markov process martingale matrix maximum likelihood estimator mean measure method Note observations obtained occur parameter Poisson process positive powerful probability problem procedure Proof properties prove random variables realization regularity relation respect sample satisfies sequence sequential shown solution space stationary statistic stochastic differential equation stochastic processes studied sufficient Suppose surely term Theorem theory transition probabilities values variance vector Wiener process zero