Embedded Markov Chain Approximations in Skorokhod Topologies

• Autorzy: Böttcher Björn

Identyfikatory

DOI

10.19195/0208-4147.39.2.2

• Języki publikacji: EN

Abstrakty

EN

We prove a J₁-tightness condition for embedded Markov chains and discuss four Skorokhod topologies in a unified manner. 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 a 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 multistep 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. For the converse statement, a J₁-tightness condition for embedded time-homogeneous Markov chains is given. Additionally, it is shown that J₁ convergence is equivalent to the joint convergence in M₁ and J₂.

Słowa kluczowe

EN

Markov chain embedding; tightness; Skorokhod space; Skorokhod topologies; jump processes; Markov chain approximation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 259--277
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Böttcher Björn

• TU Dresden, Fachrichtung Mathematik, Institut für Mathematische Stochastik, 01062 Dresden, Germany

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).