Bimonotone Brownian Motion

TL;DR

This paper introduces bi-monotone independence, establishes a central limit theorem for it, and explores the properties of bi-monotone Brownian motion, a two-dimensional process combining monotone and antimonotone Brownian motions.

Contribution

It defines bi-monotone independence, proves a central limit theorem for it, and studies the resulting bi-monotone Brownian motion, advancing non-commutative probability theory.

Findings

Bi-monotone independence is formally defined.

A central limit theorem for bi-monotone independence is proved.

Distributional properties of bi-monotone Brownian motion are analyzed.

Abstract

We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone Brownian motion as components.