Rates of Decay and h-Processes for One Dimensional Diffusions Conditioned on Non-Absorption

Servet Martínez () and Jaime San Martín ()
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Servet Martínez: Universidad de Chile
Jaime San Martín: Universidad de Chile

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 199-212

Abstract: Abstract Let (X t ) be a one dimensional diffusion corresponding to the operator $$\mathcal{L} = \tfrac{1}{2}\partial _{xx} - \alpha \partial _x$$ , starting from x>0 and T 0 be the hitting time of 0. Consider the family of positive solutions of the equation $${\mathcal{L}}\psi = - \lambda \psi$$ with λ∈(0, η), where $$\eta {\text{ = }} - \lim _{t \to \infty } (1/t){\text{ log }}\mathbb{P}_x (T_0 > t)$$ . We show that the distribution of the h-process induced by any such ψ is $$\lim _{M \to \infty } \mathbb{P}_x (X \in A|S_M

Keywords: one-dimensional diffusions; h-processes; absorption (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1007881317492

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