Abstract
Our next goal is to present the most basic notions and results from the theory of discrete- and continuous-time Markov chains. As expected, the emphasis is put here on these properties that are relevant from the viewpoint of credit risk modeling. Throughout this chapter, we fix an underlying probability space (Ω, G, ℚ), as well as a finite set K = {1,..., K}, which plays the role of the state space for all considered Markov chains. Since the state space is finite, it is clear that any function h: K → ℝ is bounded and measurable, provided that we endow the state space with the σ-field of all its subsets.
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© 2004 Springer-Verlag Berlin Heidelberg
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Bielecki, T.R., Rutkowski, M. (2004). Markov Chains. In: Credit Risk: Modeling, Valuation and Hedging. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04821-4_11
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DOI: https://doi.org/10.1007/978-3-662-04821-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08707-3
Online ISBN: 978-3-662-04821-4
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