Product space for two processes with independent increments under nonlinear expectations

TL;DR

This paper develops a framework for constructing a product space of two processes with independent increments under nonlinear expectations, enabling new analysis tools for such processes.

Contribution

It introduces a discretization method to build a nonlinear expectation where two independent increment processes form a new process with independent increments.

Findings

Constructed a product space for two processes with independent increments.

Developed a discretization approach for nonlinear expectations.

Established that the new process retains independent increments.

Abstract

In this paper, we consider the product space for two processes with independent increments under nonlinear expectations. By introducing a discretization method, we construct a nonlinear expectation under which the given two processes can be seen as a new process with independent increments.