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

Author

Listed:
  • Servet Martínez

    (Universidad de Chile)

  • Jaime San Martín

    (Universidad de Chile)

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

Suggested Citation

  • Servet Martínez & Jaime San Martín, 2001. "Rates of Decay and h-Processes for One Dimensional Diffusions Conditioned on Non-Absorption," Journal of Theoretical Probability, Springer, vol. 14(1), pages 199-212, January.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:1:d:10.1023_a:1007881317492
    DOI: 10.1023/A:1007881317492
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