G-L\'{e}vy Processes under Sublinear Expectations

TL;DR

This paper develops the theory of G-Lévy processes within sublinear expectation frameworks, establishing foundational formulas and existence results for these processes, including G-Poisson processes.

Contribution

It introduces G-Lévy processes under sublinear expectations, deriving the Lévy-Khintchine formula and proving their existence, which extends classical stochastic process theory.

Findings

Established the Lévy-Khintchine formula for G-Lévy processes

Proved the existence of G-Lévy processes under sublinear expectations

Introduced G-Poisson processes as a new class of stochastic processes

Abstract

We introduce G-L\'{e}vy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the L\'{e}vy-Khintchine formula and the existence for G-L\'{e}vy processes. We also introduce G-Poisson processes.