Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion

TL;DR

This paper establishes the existence of relaxed optimal controls for G-neutral stochastic functional differential equations driven by G-Brownian motion, with a focus on theoretical proof and numerical analysis.

Contribution

It proves the existence and uniqueness of solutions for G-NSFDEs with relaxed controls and uncontrolled diffusion, using tightness and weak convergence techniques.

Findings

Existence of an optimal relaxed control for G-NSFDEs.

Application of tightness and weak convergence methods.

Numerical analysis for uncontrolled G-NSFDEs.

Abstract

In this paper, we study the question of existence and uniqueness of solution of neutral stochastic functional differential equations driven by G- Brownian motion (GNSFDEs in short) on Banach space driven by relaxed controls in which the neutral term and diffusion do not depend on the control variable. By using tightness techniques and the weak convergence techniques for each probability measure in the set of all possible probabilities of our dynamic, we prove the existence of an optimal relaxed control. A motivation of are work is presented and a Numerical analysis for the uncontrolled G-NSFDE is given.