@article{ECP1825,
author = {Aleksandar Mijatovic and Mikhail Urusov},
title = {Convergence of integral functionals of one-dimensional diffusions},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {17},
year = {2012},
keywords = {Integral functional; one-dimensional diffusion; local time; Bessel process; Ray-Knight theorem; Williams theorem},
abstract = {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.
},
pages = {no. 61, 1-13},
issn = {1083-589X},
doi = {10.1214/ECP.v17-1825},
url = {http://ecp.ejpecp.org/article/view/1825}}