A Complex Version of G-Expectation and its Application to Conformal Martingale

TL;DR

This paper develops a complex extension of G-expectation, introduces conformal G-Brownian motion, and explores its properties and invariance, linking stochastic analysis with complex analysis.

Contribution

It introduces a complex version of G-expectation and conformal G-Brownian motion, expanding the framework of G-stochastic analysis into the complex domain.

Findings

Introduction of complex G-expectation framework

Definition and representation of conformal G-Brownian motion

Establishment of conformal invariance properties

Abstract

This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic analysis in this framework. Furthermore, the conformal G-Brownian Motion is introduced together with a representation, and the corresponding conformal invariance is shown.