Brownian Motions on Metric Graphs II - Construction of Brownian Motions on Single Vertex Graphs

TL;DR

This paper presents a comprehensive method for constructing Brownian motions on single vertex graphs that adhere to all boundary conditions, expanding the understanding of stochastic processes on complex graph structures.

Contribution

It introduces a pathwise construction technique for Brownian motions on single vertex graphs satisfying all boundary conditions, filling a gap in stochastic process theory.

Findings

Constructed Brownian motions satisfy all boundary conditions.

Provided explicit pathwise construction methods.

Enhanced understanding of stochastic processes on graphs.

Abstract

Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of single vertex graphs are given.