# 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} }

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…

## 59 Citations

### Variations of the solution to a stochastic heat equation II

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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…

### A change of variable formula with Itô correction term

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