Variations of the solution to a stochastic heat equation

@article{Swanson2007VariationsOT,
  title={Variations of the solution to a stochastic heat equation},
  author={Jason Swanson},
  journal={Annals of Probability},
  year={2007},
  volume={35},
  pages={2122-2159}
}
  • Jason Swanson
  • Published 31 December 2005
  • Mathematics
  • Annals of Probability
We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F(t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartin-gale. It follows that the classical Ito calculus does not apply. Motivated by heuristic ideas about a possible new calculus for this process, we are led to study modifications of the quadratic… 

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