# Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures

## TL;DR

This paper establishes existence and uniqueness of solutions for a broad class of semilinear SPDEs driven by Wiener processes and Poisson measures, using the 'method of the moving frame' to reduce SPDEs to SDEs.

## Contribution

It introduces refinements in existence results for SPDEs, applying the 'method of the moving frame' to handle general conditions.

## Key findings

- Proves existence and uniqueness of solutions under local Lipschitz and growth conditions.
- Reduces SPDE problems to SDE problems via the 'method of the moving frame'.
- Handles both global and local solutions for semilinear SPDEs.

## Abstract

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear growth (or local boundedness, resp.) conditions. The so-called "method of the moving frame" allows us to reduce the SPDE problems to SDE problems.