# A space of generalized Brownian motion path-valued continuous functions with application

## TL;DR

This paper introduces a new space of generalized Brownian motion paths, explores integral examples, and develops an analytic Feynman integration theory for functionals on this path space.

## Contribution

It defines a novel path space for generalized Brownian motions and establishes an analytic Feynman integration framework for functionals on this space.

## Key findings

- Defined the paths space $ ext{C}_0^{ ext{gBm}}$ for generalized Brownian motions
- Presented examples of path space integrals
- Developed an analytic Feynman integration theory for functionals

## Abstract

In this paper, we introduce the paths space $\mathcal C_0^{\mathrm{gBm}}$ which is consists of generalized Brownian motion path-valued continuous functions on $[0,T]$. We next present several relevant examples of the paths space integral. We then discuss the concept of the analytic Feynman integration theory for functionals $F$ on the paths space $\mathcal C_0^{\mathrm{gBm}}$.