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Some Improved Markov Chain Convergence Rates, Fun Choi John Chan
Some Improved Markov Chain Convergence Rates, Fun Choi John Chan
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Explicit convergence rates to equilibrium are established for non reversible Markov chains not having an atom via coupling methods. We consider two Markov chains having the same transition function but different initial conditions on the same probability space, that is, a coupling. A random time is constructed so that subsequent to the random time the two processes are identical. Exploiting a shadowing condition, we show that it is possible to bound the tail distribution of the random time using only one of the chains. This bound gives the convergence rate to equilibrium for the Markov chain. The method is then …
Predictive Maturity Of Inexact And Uncertain Strongly Coupled Numerical Models, Ismail Farajpour
Predictive Maturity Of Inexact And Uncertain Strongly Coupled Numerical Models, Ismail Farajpour
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The Computer simulations are commonly used to predict the response of complex systems in many branches of engineering and science. These computer simulations involve the theoretical foundation, numerical modeling and supporting experimental data, all of which contain their associated errors. Furthermore, real-world problems are generally complex in nature, in which each phenomenon is described by the respective constituent models representing different physics and/or scales. The interactions between such constituents are typically complex in nature, such that the outputs of a particular constituent may be the inputs for one or more constituents. Thus, the natural question then arises concerning the validity …
Aperture Coupling And Penetration In Various Configurations, Jason Keen
Aperture Coupling And Penetration In Various Configurations, Jason Keen
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The problem of a slot in a perfectly conducting surface is addressed for a variety of configurations using both integral equation and transmission line techniques. The use of Bethe hole theory to model short slots is discussed and utilized where appropriate. Primary problems of discussion are a slot array, wires coupling through slots in a ground plane, and wires coupling through slots in a bent ground plane. Additionally, the use of the extended BLT formulation for incorporation of slot effects in a transmission line problem is addressed. In this manuscript, the work of Bethe is extended to include cross-aperture coupling …