1 Mathematics Department, University of Delta, Agbor, Nigeria. 2 Mathematics Department, Delta State University, Abraka, Nigeria. This study is focused on the approximate solution for the class of ...

Abstract: We focus on the noise analysis by using stochastic differential equation model as training data of deep learning. Then, we use the solution process of stochastic differential equation for ...

In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta ...

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the ...

Rough path theory provides a rigorous framework to analyse differential equations driven by highly irregular signals, such as those encountered in stochastic differential equations (SDEs). By ...

Abstract: In this article, we consider a linear-quadratic optimal control problem of mean-field stochastic differential equation with jump diffusion, which is also called as an mean-field ...

This study develops a unified framework for optimal portfolio selection in jump–uncertain stochastic markets, contributing both theoretical foundations and computational insights. We establish the ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...