Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.7
Journals
Symmetry
Special Issues
Stochastic Differential Equations: Theory, Methods, and Applications
share announcement

Stochastic Differential Equations: Theory, Methods, and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 6980

Special Issue Editor

Dr. Marek T. Malinowski

E-Mail Website
Guest Editor
Department of Applied Mathematics, Tadeusz Kościuszko Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
Interests: stochastic differential equations; stochastic processes; probability theory; fuzzy analysis; set-valued analysis; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Stochastic differential equations constitute a powerful mathematical apparatus for dealing with phenomena whose evolution is governed by random forces. Stochastic models involving such equations are used in many areas—for example, in physics, molecular biology, finance, climatology, ocean science, electrical engineering, and mechanics. Trajectories of solutions of stochastic differential equations determine the paths of the processes studied. The practical nature of these equations is not separated from theory; the two go hand in hand. Problems of existence of the solution, its uniqueness, its properties, asymptotic behavior, approximate solution, control of solution, numerical methods, and symmetry methods are just a few of the issues deserving a mention.

Therefore, this Special Issue invites articles on recent advances in both broad aspects of stochastic differential equations, namely, in theory and applications.

Dr. Marek T. Malinowski
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • ordinary, partial, functional, backward stochastic differential equations driven by Wiener, Gaussian, Levy, stable processes, martingales, semimartingales, fractional Brownian motion
  • theory of symmetry for stochastic differential equations
  • symmetric stochastic differential equations
  • properties of solution, strong solution, weak solution, mild solution, invariance
  • stochastic integrals
  • random attractors
  • numerical solutions and methods
  • parameter estimation
  • optimal control
  • nonlinear filtering
  • applications in science and engineering

Published Papers (7 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

15 pages, 926 KiB  
Article
Stochastic Dynamics Analysis of Epidemic Models Considering Negative Feedback of Information
by Wanqin Wu, Wenhui Luo, Hui Chen and Yun Zhao
Symmetry 2023, 15(9), 1781; https://doi.org/10.3390/sym15091781 - 18 Sep 2023
Viewed by 567
Abstract
In this article, we mainly consider the dynamic analysis of a stochastic infectious disease model with negative feedback, a symmetric and compatible distribution family. Based on the sir epidemic model taking into account the isolation (y) and the death (v), we consider adding [...] Read more.
In this article, we mainly consider the dynamic analysis of a stochastic infectious disease model with negative feedback, a symmetric and compatible distribution family. Based on the sir epidemic model taking into account the isolation (y) and the death (v), we consider adding a new variable (w) to control the information of non-drug interventions, which measures transformations in isolation performance that determine the epidemic, and establish a new model. We have demonstrated various properties of the model solution using Lyapunov functions for this model. To begin with, we demonstrate the existence and uniqueness of the global positive solution. After that, we obtained the conditions that need to be met for the extinction of the disease and verified the correctness of the conclusion by simulating numerical values. Afterwards, we prove the stochastic boundedness and stationary distribution of the model solution. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

13 pages, 7812 KiB  
Article
Modelling a Market Society with Stochastically Varying Money Exchange Frequencies
by Maria Letizia Bertotti, Bruno Carbonaro and Marco Menale
Symmetry 2023, 15(9), 1751; https://doi.org/10.3390/sym15091751 - 13 Sep 2023
Viewed by 536
Abstract
We propose and examine a model expressed by stochastic differential equations for the evolution of a complex system. We refer in particular to a market society, in which the state of each individual is identified by the amount of money at his/her disposal. [...] Read more.
We propose and examine a model expressed by stochastic differential equations for the evolution of a complex system. We refer in particular to a market society, in which the state of each individual is identified by the amount of money at his/her disposal. The evolution of such a system over time is described by suitable equations that link the instantaneous changes in the probability of each state with the probable outcomes of pairwise interactions between elements of the system. In the context at hand, these pairwise interactions simply represent money exchanges, due to the sales and purchases of goods and services. In this paper, unlike the usual method in the literature, the interaction frequencies and the consequent probabilities of passing from one state to another are not considered as assigned once and for all but are supposed to be randomly variable. This choice, as also shown by several numerical simulations, seems likely to have fruitful consequences, especially for a more realistic representation of economic issues and phenomena. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

22 pages, 483 KiB  
Article
A Spectral Method Approach to Quadratic Normal Volatility Diffusions
by Peter Kink
Symmetry 2023, 15(8), 1474; https://doi.org/10.3390/sym15081474 - 25 Jul 2023
Cited by 1 | Viewed by 574
Abstract
This paper is concerned with the quadratic volatility family of driftless stochastic differential equations (SDEs), also known in the literature as Quadratic Normal Volatility models (QNV), which have found applications primarily in mathematical finance, but can also model dynamics of stochastic processes in [...] Read more.
This paper is concerned with the quadratic volatility family of driftless stochastic differential equations (SDEs), also known in the literature as Quadratic Normal Volatility models (QNV), which have found applications primarily in mathematical finance, but can also model dynamics of stochastic processes in other fields such as mathematical biology and physics. These SDE models are characterized by a quadratic volatility term and can be reduced to one of four distinct possibilities depending on the roots of the quadratic volatility term and the position of initial value. We find explicit weak solutions for each case by a combination of Itô calculus and Fourier analysis, which can be described as a ’spectral method’. Furthermore, for all cases we also express the weak solutions as fairly simple functions of Brownian motion, which allows for efficient one-step Monte Carlo evaluation of functionals of the solutions Xt of the form E(f(Xt)) and also more general functionals of the solution. The method used to compute the solutions may also be of interest itself more generally in other fields where SDEs play a fundamental role. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

25 pages, 405 KiB  
Article
Symmetric Fuzzy Stochastic Differential Equations Driven by Fractional Brownian Motion
by Hossein Jafari and Marek T. Malinowski
Symmetry 2023, 15(7), 1436; https://doi.org/10.3390/sym15071436 - 17 Jul 2023
Cited by 2 | Viewed by 666
Abstract
We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-life hybrid systems, which include [...] Read more.
We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-life hybrid systems, which include properties of being both random and fuzzy and reflecting long-range dependence. By imposing on the mappings occurring in the equation the conditions of Lipschitzian continuity and additional constraints by an integrable stochastic process, we construct an approximation sequence of fuzzy stochastic processes and apply this to prove the existence of a unique solution to the studied equation. Finally, a model from population dynamics is considered to illustrate the potential application of our equations. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

8 pages, 5605 KiB  
Article
Impact of Delay on Stochastic Predator–Prey Models
by Abdelmalik Moujahid and Fernando Vadillo
Symmetry 2023, 15(6), 1244; https://doi.org/10.3390/sym15061244 - 12 Jun 2023
Cited by 1 | Viewed by 903
Abstract
Ordinary differential equations (ODE) have long been an important tool for modelling and understanding the dynamics of many real systems. However, mathematical modelling in several areas of the life sciences requires the use of time-delayed differential models (DDEs). The time delays in these [...] Read more.
Ordinary differential equations (ODE) have long been an important tool for modelling and understanding the dynamics of many real systems. However, mathematical modelling in several areas of the life sciences requires the use of time-delayed differential models (DDEs). The time delays in these models refer to the time required for the manifestation of certain hidden processes, such as the time between the onset of cell infection and the production of new viruses (incubation periods), the infection period, or the immune period. Since real biological systems are always subject to perturbations that are not fully understood or cannot be explicitly modeled, stochastic delay differential systems (SDDEs) provide a more realistic approximation to these models. In this work, we study the predator–prey system considering three time-delay models: one deterministic and two types of stochastic models. Our numerical results allow us to distinguish between different asymptotic behaviours depending on whether the system is deterministic or stochastic, and in particular, when considering stochasticity, we see that both the nature of the stochastic systems and the magnitude of the delay play a crucial role in determining the dynamics of the system. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

24 pages, 1083 KiB  
Article
General Time-Symmetric Mean-Field Forward-Backward Doubly Stochastic Differential Equations
by Nana Zhao, Jinghan Wang, Yufeng Shi and Qingfeng Zhu
Symmetry 2023, 15(6), 1143; https://doi.org/10.3390/sym15061143 - 24 May 2023
Viewed by 1708
Abstract
In this paper, a general class of time-symmetric mean-field stochastic systems, namely the so-called mean-field forward-backward doubly stochastic differential equations (mean-field FBDSDEs, in short) are studied, where coefficients depend not only on the solution processes but also on their law. We first verify [...] Read more.
In this paper, a general class of time-symmetric mean-field stochastic systems, namely the so-called mean-field forward-backward doubly stochastic differential equations (mean-field FBDSDEs, in short) are studied, where coefficients depend not only on the solution processes but also on their law. We first verify the existence and uniqueness of solutions for the forward equation of general mean-field FBDSDEs under Lipschitz conditions, and we obtain the associated comparison theorem; similarly, we also verify those results about the backward equation. As the above two comparison theorems’ application, we prove the existence of the maximal solution for general mean-field FBDSDEs under some much weaker monotone continuity conditions. Furthermore, under appropriate assumptions we prove the uniqueness of the solution for the equations. Finally, we also obtain a comparison theorem for coupled general mean-field FBDSDEs. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

16 pages, 407 KiB  
Article
Dynamics Analysis of a Class of Stochastic SEIR Models with Saturation Incidence Rate
by Pengpeng Liu and Xuewen Tan
Symmetry 2022, 14(11), 2414; https://doi.org/10.3390/sym14112414 - 15 Nov 2022
Cited by 2 | Viewed by 1180
Abstract
In this article, a class of stochastic SEIR models with saturation incidence is studied. The model is a symmetric and compatible distribution family. This paper studies various properties of the system by constructing Lyapunov functions. First, the gradual properties of the systematic solution [...] Read more.
In this article, a class of stochastic SEIR models with saturation incidence is studied. The model is a symmetric and compatible distribution family. This paper studies various properties of the system by constructing Lyapunov functions. First, the gradual properties of the systematic solution near the disease-free equilibrium of the deterministic model is studied, followed by the final behavior of the model, including stochastic persistence and final extinction. Finally, the existence conditions of the stationary distribution of the model are given, and then it is proved that it is traversed, and the corresponding conclusions are verified through numerical simulation. Full article
(This article belongs to the Special Issue Stochastic Differential Equations: Theory, Methods, and Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-7
Back to TopTop