Accelerated Accuracy in the Simulation of Markov Chains

Article Abstract:

A method of obtaining results from the simulation of an n + 1 finite state positive recurrent aperiodic Markov chain is described. It can be done at a cost considerably less than that required by pure random sampling to achieve the same accuracy. The method reorganizes k independent epochs simulated serially into k replications simulated in parallel. This produces cost savings by inducing selected joint distributions across replications. The joint distributions are derived by the use of rotation sampling, a special case of the antithetic variate method. A computer program that implements the method for the general finite state case is briefly described. Tables showing empirical results are shown.

Models, Accuracy, Sampling

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Accelerated Convergence in the Simulation of Countably Infinite State Markov Chains

Article Abstract:

A method of obtaining results from the simulation of a countably infinite state, positive recurrent aperiodic Markov chain is given. The method costs considerably less than using random sampling. Rotation sampling can be combined with special structure in the chain to achieve additional variance reduction without additional cost. A table gives simulation results.

Statistics (Data), Simulation Theory, Statistics, Theory

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Mean Drifts and the Non-ergodicity of Markov Chains

Article Abstract:

An important question in stochastic modeling is whether or not a denumerable state Markov chain is ergodic. A result of Kaplan giving a condition for the non-ergodicity of a chain is extended based on its drifts. The conditions under which the mean drift in the stationary chain is zero is clarified.

Mathematical models, Optimization, Stochastic Model

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