| Título: | Convergence of integral functionals of one-dimensional diffusions |
| Autores: |
Mijatovic, Aleksandar; Imperial College Urusov, Mikhail; Universität Duisburg-Essen |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Integral functional; one-dimensional diffusion; local time; Bessel process; Ray-Knight theorem; Williams theorem 60H10; 60J60 |
| Descripción: | In this paper we describe the pathwise behaviour of the integral functional $\int_0^t f(Y_u)\,du$ for any $t\in[0,\zeta]$, where $\zeta$ is (a possibly infinite) exit time of a one-dimensional diffusion process $Y$ from its state space, $f$ is a nonnegative Borel measurable function and the coefficients of the SDE solved by $Y$ are only required to satisfy weak local integrability conditions. Two proofs of the deterministic characterisation of the convergence of such functionals are given: the problem is reduced in two different ways to certain path properties of Brownian motion where either the Williams theorem and the theory of Bessel processes or the first Ray-Knight theorem can be applied to prove the characterisation. As a simple application of the main results we give a short proof of Feller's test for explosion. |
| Idioma: | Inglés |
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