Abstract
The purpose of this chapter is to develop the theory of QSDs in the framework of one dimensional diffusions absorbed at 0. So here the space is \(\mathcal{X}=\mathbb {R}_{+}\) and the trap \({\partial\mathcal{X}}=\{0\}\). Some of the applications of this theory can be found in models of ecology, economy (see Sect. 7.8 in the next chapter) and Markov mortality models (see Steinsaltz and Evans in Theor. Popul. Biol. 65(4):319–337, 2004).
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Notes
- 1.
Given a measure ρ, the integral \(\int_{a}^{b} f(x) \,d\rho(x)\) is interpreted as the integral over the closed interval [a,b], unless a or b are ±∞ in which case they are excluded from the integral. When it is necessary to exclude, for example, the point a, we shall use the notation ∫(a,b] f(x) dρ(x).
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Collet, P., Martínez, S., San Martín, J. (2013). Regular Diffusions on [0,∞). In: Quasi-Stationary Distributions. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33131-2_6
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