Differential Equations and Stochastic Processes: Trends and Challenges

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 902

Special Issue Editor

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Guest Editor
Faculty of Science and Technology, Athabasca University, Athabasca, AB, Canada
Interests: differential equations; nonlinear analysis; variational approach and optimization; monotone operator theory; topological methods stochastic processes and their applications: optimal control problems in finance governed by stochastic differential equations (and systems)

Special Issue Information

Dear Colleagues,

Differential equations are used to model natural phenomena from various scientific fields. Many dynamic processes can be analyzed and understood through the solutions to problems expressed via differential equations. Differential equations involving a stochastic process, also known as stochastic differential equations (SDEs), can enable modeling of chaotic and random structures evolving over time at a very high level of accuracy. As such, since the first appearance of SDEs in the literature, presented by Uhlenbeck and Ornstein (1930) in their seminal work Ornstein–Uhlenbeck model of Brownian motion, the theory of SDEs has developed significantly, fueled by Itô’s contributions (1951), with applications in physics, astronomy, electronics, civil engineering, chemistry, biology, economics, finance, etc.

The aim of this Special Issue is to collect original and high-quality research and review articles related to the development, trends, and challenges in the theory of stochastic processes and its applications.

Potential topics include (but are not limited to):

  • Trends and challenges related to stochastic processes and their applications;
  • Stochastic differential equations;
  • Optimal control problems governed by stochastic differential equations (and systems);
  • Variational approach for solving stochastic differential equations;
  • Iterative algorithms for solving stochastic differential equations;
  • Numerical methods for solving stochastic differential equations.

Dr. Mustafa Avci
Guest Editor

Manuscript Submission Information

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  • stochastic processes
  • stochastic differential equations
  • variational approach
  • optimization
  • Brownian process
  • Wiener process
  • numerical methods
  • iterative algorithms

Published Papers (1 paper)

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13 pages, 296 KiB  
Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator
by Pei Zhang, Adriana Irawati Nur Ibrahim and Nur Anisah Mohamed
Mathematics 2023, 11(23), 4845; https://doi.org/10.3390/math11234845 - 01 Dec 2023
Viewed by 609
This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H(1/2,1). This [...] Read more.
This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H(1/2,1). This study expands upon the findings of the anticipated BSDE by considering the scenario when the driver is fractional Brownian motion rather instead of standard Brownian motion. Additionally, the generator incorporates not only the present and future but also the past. We will demonstrate the existence and uniqueness of the solutions to these equations by employing the fixed point theorem. Furthermore, an equivalent comparison theorem is derived. Full article
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