Multi-point local time penalizations with various clocks for one-dimensional L\'{e}vy processes

TL;DR

This paper investigates how different random clocks based on multi-point local times affect the penalization of one-dimensional Lévy processes, leading to diverse limit processes that differ from the original.

Contribution

It introduces a novel penalization framework using various clocks and analyzes the resulting limit processes, revealing their dependence on the choice of clock.

Findings

Limit processes vary with different clock choices.

Limit processes are singular to the original Lévy process.

The framework extends understanding of penalization effects on Lévy processes.

Abstract

We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional L\'{e}vy processes. The limit processes may vary according to the choice of random clock, and are singular to the original process.