| Springer Verlag, 1999 Reviewed for Metrika (2007) | |||||||||||||
Abstract | |||||||||||||
| Markov processes serve as mathematical models in applied sciences since the beginning of the 20th century. A main reason is their conceptual simplicity. Nevertheless, as a rst approximation to non-independence they exhibit a wealth of complex and qualitatively dierent behaviour and thus can explain a variety of qualitative eects, similar to ordinary dierential equations in real analysis. Though Markov chain theory is one of the basic probabilistic concepts since so many years, we witnessed a renaissance of Markov processes in recent years. As probabilistic models they penetrate elds like statistical modelling, nance and genomics. On the other hand, due to the increase of computer power, they play an increasing role in simulations and numerical algorithms. For example, Markov Chain Monte Carlo methods revolutionized Bayesian statistics and graphical methods. NP-complete optimization problems like the travelling salesman problem are attacked by means of simulated annealing. Similarly, computation of maximum likelihood estimators 1 | |||||||||||||
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