# Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions

## TL;DR

This paper develops exponential moment bounds, regularity, and convergence rates for a class of numerical schemes approximating stochastic convolutions, tailored for SPDEs with non-globally Lipschitz nonlinearities.

## Contribution

It introduces taming and truncation techniques in exponential Euler-type schemes, enabling strong convergence analysis for challenging SPDEs.

## Key findings

- Established exponential moment bounds for the schemes
- Proved uniform Hölder continuity in time
- Demonstrated strong convergence rates

## Abstract

In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical approximations of infinite dimensional stochastic convolution processes. The considered approximations involve specific taming and truncation terms and are therefore well suited to be used in the context of SPDEs with non-globally Lipschitz continuous nonlinearities.