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AN INTRODUCTION TO MARKOV CHAIN ANALYSIS
iii The limiting matrix
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absorbing Markov aspatial assumed assumption bability Central Limit theorem component computed concept cubic matrix degrees of freedom dependent derived diagonal diagonal matrix Drewett and Ferguson elements entries equilibrium estimated transition probabilities first-order Markov chain first-order property fundamental matrix homogeneity identity matrix individual movements Kemeny and Snell Krenz large number Lever likelihood ratio criterion limiting matrix loge London manufacturing establishments Markov chain analysis Markov chain models Markov model Markov process Markov property mathematical proof Maximum likelihood ratio mean first passage migrant distance migration null hypothesis number of steps observations Pacific percent period Pijk plants population pyramids predictive Principal Components Analysis probability of moving probability vector regular Markov chain relocate S2 S3 sl ships Sl S2 S3 specific-order stationarity statistical tests stochastic matrix stochastic process suburbs system of spatial Table tally matrix three oceans total number trends typify a first-order underlying fixed probabilities values variables Zone 2 Zone