Convergence of integral functionals of one-dimensional diffusions

By Aleksandar Mijatovi'c, Mikhail Urusov. 2011

51 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d3c0c4f1292b5fc589139c4eae31f0840ccf3ce

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In Finance

  1. Ioannis Karatzas
  2. J. Ruf
  3. Soumik Pal
  4. Mykhaylo Shkolnikov
  5. Constantinos Kardaras
  6. Tomoyuki Ichiba
  7. Gordan Zitkovic
  8. Marcel Nutz

In Mathematical Physics

  1. J. Ruf
  2. Ioannis Karatzas

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