Abstract
In the framework of this theory, there is a Markov process evolving in a domain where there is a set of forbidden states that constitutes a trap. The process is said to be killed when it hits the trap and it is assumed that this happens almost surely. We investigate the behavior of the process before being killed, more precisely we study what happens when one conditions the process to survive for a long time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Darroch, J. N., & Seneta, E. (1965). On quasi-stationary distributions in absorbing discrete-time finite Markov chains. Journal of Applied Probability, 2, 88–100.
Davies, B. (1989). Heat kernels and spectral theory. Cambridge: Cambridge University Press.
Gikhman, I., & Skorokhod, A. (1996). Introduction to the theory of random processes. Mineola: Dover.
Pinsky, R. (1985). On the convergence of diffusion processes conditioned to remain in bounded region for large time to limiting positive recurrent diffusion processes. Annals of Probability, 13, 363–378.
Vere-Jones, D. (1962). Geometric ergodicity in denumerable Markov chains. Quarterly Journal of Mathematics Oxford (2), 13, 7–28.
Yaglom, A. M. (1947). Certain limit theorems of the theory of branching processes. Doklady Akademii Nauk SSSR, 56, 795–798 (in Russian).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Collet, P., Martínez, S., San Martín, J. (2013). Introduction. In: Quasi-Stationary Distributions. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33131-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-33131-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33130-5
Online ISBN: 978-3-642-33131-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)