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Embedded Markov chain approximations in Skorokhod topologies by Böttcher, Björn ( Author )
Lemonjar Open Access
N.A
16-09-2014
In order to approximate a continuous time stochastic process by discrete time Markov chains one has several options to embed the Markov chains into continuous time processes. On the one hand there is the Markov embedding, which uses exponential waiting times. On the other hand each Skorokhod topology naturally suggests a certain embedding. These are the step function embedding for J1, the linear interpolation embedding for M1, the multi step embedding for J2 and a more general embedding for M2. We show that the convergence of the step function embedding in J1 implies the convergence of the other embeddings in the corresponding topologies, respectively. For the converse statement a J1-tightness condition for embedded Markov chains is given. The result relies on various representations of the Skorokhod topologies. Additionally it is shown that J1 convergence is equivalent to the joint convergence in M1 and J2.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1409.4656
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