Abstract
A rather detailed study of Markov processes with discrete state space is provided. It focuses on sample path techniques in a perspective inspired by simulation needs. The relationship of these processes with Poisson processes and with discrete-time Markov chains is shown. Rigorous constructions and results are provided for Markov process with uniformly bounded jump rates. To this end, elements of the theory of bounded operators are introduced, which explain the relation between generator and semigroup, and provide a useful framework for the forward and backward Kolmogorov equations and the Feynman–Kac formula.
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References
Anderson, W.J.: Continuous-Time Markov Chains. Springer Series in Statistics: Probability and Its Applications. Springer, New York (1991)
Asmussen, S., Glynn, P.W.: Stochastic Simulation: Algorithms and Analysis. Stochastic Modelling and Applied Probability, vol. 57. Springer, New York (2007)
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Graham, C., Talay, D. (2013). Discrete-Space Markov Processes. In: Stochastic Simulation and Monte Carlo Methods. Stochastic Modelling and Applied Probability, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39363-1_5
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DOI: https://doi.org/10.1007/978-3-642-39363-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39362-4
Online ISBN: 978-3-642-39363-1
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