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Axioms
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Advances in Stochastic Processes and Stochastic Differential Equations
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Advances in Stochastic Processes and Stochastic Differential Equations

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (27 December 2024) | Viewed by 6693

Special Issue Editor

Prof. Dr. Nikos Halidias

E-Mail Website
Guest Editor
Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, 83200 Karlovassi, Greece
Interests: differential equation; stochastic analysis; stochastic differential equation and its application in finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to contribute to this Special Issue on “Stochastic Processes and Stochastic Differential Equations”. The aim of this Special Issue is to publish high-quality papers on stochastic processes and their applications. We invite articles dealing with both discrete-time and continuous-time stochastic processes. Applications of stochastic processes can be related to financial mathematics, actuarial science, etc. 

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Stochastic Processes;
  • Markov Processes;
  • Diffusion Processes; 
  • Queueing Theory;
  • Queues;
  • Financial Mathematics.

Prof. Dr. Nikos Halidias
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. Axioms 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

  • stochastic processes
  • Markov processes
  • diffusion processes
  • queueing theory
  • queues
  • financial mathematics
  • Stochastic Differential Equations
  • Differential Equations

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

16 pages, 1257 KiB  
Article
A Novel Sine Step Size for Warm-Restart Stochastic Gradient Descent
by Mahsa Soheil Shamaee and Sajad Fathi Hafshejani
Axioms 2024, 13(12), 857; https://doi.org/10.3390/axioms13120857 - 6 Dec 2024
Cited by 1 | Viewed by 740
Abstract
This paper proposes a novel sine step size for warm-restart stochastic gradient descent (SGD). For the SGD based on the new proposed step size, we establish convergence rates for smooth non-convex functions with and without the Polyak–Łojasiewicz (PL) condition. To assess the effectiveness [...] Read more.
This paper proposes a novel sine step size for warm-restart stochastic gradient descent (SGD). For the SGD based on the new proposed step size, we establish convergence rates for smooth non-convex functions with and without the Polyak–Łojasiewicz (PL) condition. To assess the effectiveness of the new step size, we implemented it across several datasets, including FashionMNIST, CIFAR10, and CIFAR100. This implementation was compared against eight distinct existing methods. The experimental results demonstrate that the proposed sine step size improves the test accuracy of the CIFAR100 dataset by 1.14%. This improvement highlights the efficiency of the new step size when compared to eight other popular step size methods. Full article
(This article belongs to the Special Issue Advances in Stochastic Processes and Stochastic Differential Equations)
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24 pages, 566 KiB  
Article
Analysis of Tandem Queue with Multi-Server Stages and Group Service at the Second Stage
by Sergei A. Dudin, Olga S. Dudina and Alexander N. Dudin
Axioms 2024, 13(4), 214; https://doi.org/10.3390/axioms13040214 - 25 Mar 2024
Cited by 3 | Viewed by 1477
Abstract
In this paper, we consider a tandem dual queuing system consisting of multi-server stages. Stage 1 is characterized by an infinite buffer, one-by-one service of customers, and an exponential distribution of service times. Stage 2 is characterized by a finite buffer and a [...] Read more.
In this paper, we consider a tandem dual queuing system consisting of multi-server stages. Stage 1 is characterized by an infinite buffer, one-by-one service of customers, and an exponential distribution of service times. Stage 2 is characterized by a finite buffer and a phase-type distribution of service times. Service at Stage 2 is provided to groups of customers. The service time of a group depends on the size of the group. The size is restricted by two thresholds. The waiting time of a customer at each stage is limited by a random variable with an exponential distribution, with the parameter depending on the stage. After service at Stage 1, a customer can depart from the system or try to enter Stage 2. If the buffer at this stage is full, the customer is either lost or returns for service at Stage 1. Customer arrivals are described by the versatile Markov arrival process. The system is studied via consideration of a multi-dimensional continuous-time Markov chain. Numerical examples, which highlight the influence of the thresholds on the system performance measures, are presented. The possibility of solving optimization problems is illustrated. Full article
(This article belongs to the Special Issue Advances in Stochastic Processes and Stochastic Differential Equations)
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17 pages, 485 KiB  
Article
Infinite Horizon Irregular Quadratic BSDE and Applications to Quadratic PDE and Epidemic Models with Singular Coefficients
by Mhamed Eddahbi, Omar Kebiri and Abou Sene
Axioms 2023, 12(12), 1068; https://doi.org/10.3390/axioms12121068 - 21 Nov 2023
Viewed by 1434
Abstract
In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a [...] Read more.
In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the Itô–Krylov’s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts. Full article
(This article belongs to the Special Issue Advances in Stochastic Processes and Stochastic Differential Equations)
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13 pages, 350 KiB  
Article
Numerical Solution of Nonlinear Backward Stochastic Volterra Integral Equations
by Mahvish Samar, Kutorzi Edwin Yao and Xinzhong Zhu
Axioms 2023, 12(9), 888; https://doi.org/10.3390/axioms12090888 - 18 Sep 2023
Cited by 3 | Viewed by 1954
Abstract
This work uses the collocation approximation method to solve a specific type of backward stochastic Volterra integral equations (BSVIEs). Using Newton’s method, BSVIEs can be solved using block pulse functions and the corresponding stochastic operational matrix of integration. We present examples to illustrate [...] Read more.
This work uses the collocation approximation method to solve a specific type of backward stochastic Volterra integral equations (BSVIEs). Using Newton’s method, BSVIEs can be solved using block pulse functions and the corresponding stochastic operational matrix of integration. We present examples to illustrate the estimate analysis and to demonstrate the convergence of the two approximating sequences separately. To measure their accuracy, we compare the solutions with values of exact and approximative solutions at a few selected locations using a specified absolute error. We also propose an efficient method for solving a triangular linear algebraic problem using a single integral equation. To confirm the effectiveness of our method, we conduct numerical experiments with issues from real-world applications. Full article
(This article belongs to the Special Issue Advances in Stochastic Processes and Stochastic Differential Equations)
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