Abstract
In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a given Markov process by Markov chains.
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Notes
(C1) is assumed to hold for each chain \(\{X^{n}_{t}\}_{t\geq 0}\) by replacing the kernel \(k(x,y)\) by \(C^{n}(a,b)\).
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Acknowledgements
Financial support through the Croatian Science Foundation (under Project 3526) (for Ante Mimica), the Croatian Science Foundation (under Project 3526) and the Dresden Fellowship Programme (for Nikola Sandrić) is gratefully acknowledged.
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Ante Mimica is deaceased, 1981-01-20–2016-06-09.
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Mimica, A., Sandrić, N. & Schilling, R.L. Markov Chain Approximation of Pure Jump Processes. Acta Appl Math 158, 167–206 (2018). https://doi.org/10.1007/s10440-018-0179-9
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DOI: https://doi.org/10.1007/s10440-018-0179-9
Keywords
- Non-symmetric Dirichlet form
- Non-symmetric Hunt process
- Markov chain
- Mosco convergence
- Semimartingale
- Semimartingale characteristics
- Weak convergence