On universality in penalisation problems with multiplicative weights

TL;DR

This paper introduces a broad framework for understanding universality classes in penalisation problems involving multiplicative weights across various stochastic processes.

Contribution

It provides a general theoretical framework applicable to Brownian motions, Lévy processes, and Langevin processes, unifying diverse penalisation problems.

Findings

Unified framework for universality classes in penalisation problems.

Applicable to multiple stochastic processes including Brownian, Lévy, and Langevin.

Enhances understanding of measure behaviors in penalisation contexts.

Abstract

We give a general framework for the universality classes of $ \sigma $-finite measures in penalisation problems with multiplicative weights. We discuss penalisation problems for Brownian motions, L\'evy processes and Langevin processes in our framework.