On a new version of the Ito's formula for the stochastic heat equation

Alberto Lanconelli

On a new version of the Ito's formula for the stochastic heat equation

Probability 2007-05-23 v1

Authors: Alberto Lanconelli

Abstract

We derive an It\^o's-type formula for the one dimensional stochastic heat equation driven by a space-time white noise. The proof is based on elementary properties of the $\mathcal{S}$ -transform and on the explicit representation of the solution process. We also discuss the relationship with other versions of this It\^o's-type formula existing in literature.

Keywords

Itô's formula stochastic heat equation space-time white noise $\mathcal{S}$-transform stochastic partial differential equations

Cite

@article{arxiv.0704.2018,
  title  = {On a new version of the Ito's formula for the stochastic heat equation},
  author = {Alberto Lanconelli},
  journal= {arXiv preprint arXiv:0704.2018},
  year   = {2007}
}

Comments

10 pages

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