The probabilistic scaling paradigm

TL;DR

This paper discusses the probabilistic scaling approach by comparing its application to the stochastic heat, nonlinear wave, and nonlinear Schrödinger equations through a case study.

Contribution

It provides a detailed analysis of probabilistic scaling across different stochastic PDEs, extending previous work with new case studies.

Findings

Probabilistic scaling applies to multiple stochastic PDEs.

Comparison reveals similarities and differences in behavior.

Insights into the applicability of probabilistic methods.

Abstract

In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrodinger equation.