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Article overview
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Convergence of Integral Functionals of One-Dimensional Diffusions | Aleksandar Mijatović
; Mikhail Urusov
; | Date: |
1 Sep 2011 | Abstract: | In this expository paper we describe the pathwise behaviour of the integral
functional $int_0^t f(Y_u),dd u$ for any $tin[0,zeta]$, 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. | Source: | arXiv, 1109.0202 | Services: | Forum | Review | PDF | Favorites |
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