Markov approximation analysis

The difference between the Markov model lineshapes and those from the Smoluchowski model is particularly pronounced when the diffusion coefficient is of the order of the quadrupole coupling constant. In the limit of large diffusion coefficients, the two models converge, and in the limit of low diffusion coefficients, the spectra are dominated by small-amplitude oscillations within potential wells, which can be approximately modelled by a suitable Markov model. This work strongly suggests that there could well be cases where analysis of powder pattern lineshapes with a Markov model leads to a fit between experimental and simulated spectra but where the fit model does not necessarily describe the true dynamics in the system. 

White, D. J. (1980b), Finite-State Approximations for Denumerable-State Infinite-Horizon Discounted Markov Decision Processes, Journal of Mathematical Analysis and Applications, Vol. 74, pp. 292-295. 

Whitt, W. (1979a), A-Piiori Bounds for Approximations of Markov Programs, matical Analysis and Applications, Vol. 71, pp. 297-302. 

Stimulation, environmental vs. task, 1357, 1358 STL (stereo lithography format), 208 Stochastic approximation, 2634-2635 Stochastic counterpart method, 2635 Stochastic decision trees, 2384, 2385 Stochastic models, 2146-2170 benefits of mathematical analysis of, 2146 definition of, 2146, 2150 Markov chains, 2150-2156 in continuous time, 2154-2156 and Markov property, 2150-2151 queueing model based on, 2153-2154... 

In the implementation of LS for this work, the method based on the normalized center of mass of the failure domain F has been employed, because it relies on a map approximating the failiue domain F under analysis (given by the failure samples generated through a Markov chain) and thus it provides in... 

Ou, Y. and J. Bechta-Dugan (2003). Approximate sensitivity analysis for acyclic Markov reliability models. IEEE Transactions on Reliability 52(2), 220-231. 

The Markov analysis is primarily used to assess the transition from one condition to another. The formula for the safety architectures in the informative part 6 of lEC 61508 was derived from such models. Those formulas are gladly used for the EE safety architectures. However, the basic principles and assumptions, under which the models were designed and the formulas derived, are often not known or not applicable for the realized automotive architectures. Often only one failure at the time is assumed, therefore ageing affects, error combinations, dependent, transient or latent failures are not derivable from this formula. For approximations or as help for the quantification these formulas are applicable if corresponding further analyses are applied. 

The problem of time variant reliability analysis of nonlinear dynamical systems can be studied to a limited extent through analytical methods and more comprehensively with simulation-based strategies. The analytical approximations are based on theory of outcrossing statistics and Markov vector approaches. Monte Carlo simulation-based methods invariably need to be reinforced with suitable variance reduction strategies so that the resulting tools become applicable to tackle... 

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