Tugrul Dayar's Analyzing Markov Chains using Kronecker Products: Theory and PDF

By Tugrul Dayar

Kronecker items are used to outline the underlying Markov chain (MC) in quite a few modeling formalisms, together with compositional Markovian versions, hierarchical Markovian types, and stochastic method algebras. the incentive in the back of utilizing a Kronecker established illustration instead of a flat one is to relieve the garage specifications linked to the MC. With this technique, structures which are an order of significance greater should be analyzed at the related platform. The advancements within the answer of such MCs are reviewed from an algebraic standpoint and attainable parts for extra study are indicated with an emphasis on preprocessing utilizing reordering, grouping, and lumping and numerical research utilizing block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic tools. Case stories from closed queueing networks and stochastic chemical kinetics are supplied to inspire decompositional and matrix analytic tools, respectively.

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