Abstract
We first introduce some practical and theoretical issues of modeling by means of Markov processes. Point processes are introduced in order to model jump instants. The Poisson process is then characterized as a point process without memory. The rest of the chapter consists in its rather detailed study, including various results concerning its simulation and approximation. This study is essential to understand the abstract constructions and the simulation methods for jump Markov processes developed in the following chapters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York (1999)
Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus, 2nd edn. Graduate Texts in Mathematics, vol. 113. Springer, New York (1991)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Graham, C., Talay, D. (2013). Poisson Processes as Particular 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_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-39363-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39362-4
Online ISBN: 978-3-642-39363-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)