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09 February 2025
 
  » arxiv » 1109.0202

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Convergence of Integral Functionals of One-Dimensional Diffusions
Aleksandar Mijatović ; Mikhail Urusov ;
Date 1 Sep 2011
AbstractIn 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
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