A change of variable formula with Itô correction term

@article{Burdzy2010ACO,
  title={A change of variable formula with It{\^o} correction term},
  author={K. Burdzy and J. Swanson},
  journal={Annals of Probability},
  year={2010},
  volume={38},
  pages={1817-1869}
}
  • K. Burdzy, J. Swanson
  • Published 2010
  • Mathematics
  • Annals of Probability
  • We consider the solution u(x, t) to a stochastic heat equation. For fixed x, the process F(t) = u(x, t) has a nontrivial quartic variation. It follows that F is not a semimartingale, so a stochastic integral with respect to F cannot be defined in the classical Ito sense. We show that for sufficiently differentiable functions g(x, t), a stochastic integral ∫ g(F(t), t) d F(t) exists as a limit of discrete, midpoint-style Riemann sums, where the limit is taken in distribution in the Skorokhod… CONTINUE READING
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