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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

Diffusions from Infinity

Résumé

In this paper we consider diffusions on the half line (0, ∞) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This implies that there is a well defined diffusion process starting from infinity, which takes finite values at positive times. We study the behaviour of hitting times of large barriers and in a dual way, the behaviour of the process starting at infinity for small time. In particular we prove that the process coming down from infinity is in small time governed by a specific deterministic function. Suitably normalized fluctuations of the hitting times are asymptotically Gaussian. We also derive the tail of the distribution of the hitting time of the origin and a Yaglom limit for the diffusion starting from infinity. We finally prove that the distribution of this process killed at the origin is absolutely continuous with respect to the speed measure. The density is expressed in terms of the eigenvalues and eigenfunctions of the generator of the killed diffusion.
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Dates et versions

hal-01639034 , version 1 (20-11-2017)

Identifiants

Citer

Vincent Bansaye, Pierre Collet, Servet Martinez, Sylvie Méléard, Jaime San Martin. Diffusions from Infinity. Transactions of the American Mathematical Society, 2019, 372 (8), pp.5781-5823. ⟨10.1090/tran/7841⟩. ⟨hal-01639034⟩
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