A mild Ito formula for SPDEs

TL;DR

This paper introduces mild Ito processes, a class of stochastic processes including mild solutions of SPDEs, and presents a new Ito formula applicable to these processes, facilitating analysis and numerical approximation.

Contribution

It proposes a novel mild Ito formula for mild Ito processes, expanding tools for analyzing SPDEs and their numerical schemes.

Findings

The new Ito formula applies to mild solutions of SPDEs.

It enables better analysis of numerical approximation processes.

The framework simplifies handling stochastic partial differential equations.

Abstract

This article introduces a certain class of stochastic processes, which we suggest to call mild Ito processes, and a new - somehow mild - Ito type formula for such processes. Examples of mild Ito processes are mild solutions of SPDEs and their numerical approximation processes.