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Axioms
Special Issues
Stochastic Processes: Theory and Application
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Stochastic Processes: Theory and Application

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 8872

Special Issue Editor

Dr. Qingan Qiu

E-Mail Website
Guest Editor
Department of Management Science and Engineering, School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
Interests: stochastic modeling; risk analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

You are kindly invited to contribute to this Special Issue on “Stochastic Processes: Theory and Applications”. This Special Issue focuses on advances in the theory of the stochastic process and its practical applications in a broad spectrum of mathematical, scientific, and engineering interests. It invites studies proposing new stochastic processes, models, as well as methods to capture dynamic phenomena in various research areas. Submissions addressing fundamental research questions are highly encouraged. Some possible topics of interest include—but are not limited to—the following fields:

  • Decision-making optimization under uncertainty;
  • Risk management and control;
  • Statistical learning based on advanced stochastic methods;
  • Stochastic game;
  • Reliability modeling and maintenance optimization;
  • Queueing models;
  • Computational methods for stochastic models;
  • Stochastic processes in mathematical finance.

Dr. Qingan Qiu
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
  • stochastic modeling
  • risk analysis
  • optimization under uncertainty

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Published Papers (4 papers)

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Research

12 pages, 431 KiB  
Article
A Numerical Approach of Handling Fractional Stochastic Differential Equations
by Iqbal M. Batiha, Ahmad A. Abubaker, Iqbal H. Jebril, Suha B. Al-Shaikh and Khaled Matarneh
Axioms 2023, 12(4), 388; https://doi.org/10.3390/axioms12040388 - 17 Apr 2023
Cited by 9 | Viewed by 2278
Abstract
This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, a novel three-point fractional formula for approximating the Riemann–Liouville integrator is established, and then it is applied to generate approximate solutions for fractional stochastic differential equations. Such [...] Read more.
This work proposes a new numerical approach for dealing with fractional stochastic differential equations. In particular, a novel three-point fractional formula for approximating the Riemann–Liouville integrator is established, and then it is applied to generate approximate solutions for fractional stochastic differential equations. Such a formula is derived with the use of the generalized Taylor theorem coupled with a recent definition of the definite fractional integral. Our approach is compared with the approximate solution generated by the Euler–Maruyama method and the exact solution for the purpose of verifying our findings. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Application)
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17 pages, 2011 KiB  
Article
Customizing Random Replacement Model and Flexible Warranty Model from the Perspective of Screening Reliability
by Lijun Shang, Baoliang Liu, Li Yang and Kaiye Gao
Axioms 2023, 12(4), 358; https://doi.org/10.3390/axioms12040358 - 7 Apr 2023
Cited by 3 | Viewed by 1587
Abstract
In the present academic and engineering fields, every measure function of product reliability is modeled and estimated from the statistical perspective. These indicate that there universally exist differences in the reliabilities of new identical products that survive the burn-in test. On the basis [...] Read more.
In the present academic and engineering fields, every measure function of product reliability is modeled and estimated from the statistical perspective. These indicate that there universally exist differences in the reliabilities of new identical products that survive the burn-in test. On the basis of the differences in the reliabilities of new identical products, designing through-life maintenance models for managing the different reliabilities is a very practical topic for engineering fields. In this study, a random warranty model and a random maintenance model are designed by screening product reliabilities to manage the through-life reliabilities of products. In the random warranty model, the coverage areas of the warranty are set as the different areas for applying flexibility to them to control the warranty costs of new identical products with different reliabilities, and thus this warranty is called a flexible random free repair warranty (FRFRW) model. In the random maintenance model, two random replacement actions are customized by setting different replacement ranges for controlling maintenance costs and lengthening service life. This random maintenance model is called a customized random replacement (CRR), which is used to manage product reliabilities after the FRFRW expiration. These two random models are characterized from the mathematical perspective, and some derivatives of both are provided to model other maintenance problems. The characteristics of every model and the performance of the CRR are explored and illustrated through numerical experiments. The results show that the CRR is superior to random age replacement. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Application)
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17 pages, 1084 KiB  
Article
Study of a Random Warranty Model Maintaining Fairness and a Random Replacement Next Model Sustaining Post-Warranty Reliability
by Lifeng Shang, Nan Zhang, Li Yang and Lijun Shang
Axioms 2023, 12(3), 258; https://doi.org/10.3390/axioms12030258 - 2 Mar 2023
Cited by 2 | Viewed by 1206
Abstract
With the help of advanced digital technologies, product managers can use monitored mission cycles to sustain product reliability. In this study, a random warranty model and a random replacement next (RRN) model are designed to sustain the through-life reliability of the product with [...] Read more.
With the help of advanced digital technologies, product managers can use monitored mission cycles to sustain product reliability. In this study, a random warranty model and a random replacement next (RRN) model are designed to sustain the through-life reliability of the product with monitored mission cycles. The designed random warranty, called a two-stage two-dimensional free repair warranty (2DFRW), can be carried out to sustain the reliability of the product during the warranty stage. In this warranty, ‘whichever occurs first and last’ is used to distinguish the coverage ranges of the latter stage warranties, which is to maintain the warranty fairness by removing the inequity of the former stage warranty. The RRN can be performed to sustain post-warranty reliability, which defines that if the limited number of mission cycles is completed before a working time, then the product will be replaced at next mission cycle completion to extend remaining service life; otherwise, the product will be replaced at a working time. Under the case of the two-stage 2DFRW, the cost rate of the RRN is constructed based on the renewable reward theorem. By simplifying the parameters, some derivative models of the cost rate are presented. Numerical analysis is performed to explore characteristics. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Application)
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11 pages, 1572 KiB  
Article
Reliability Evaluation and Optimization of a System with Mixed Run Shock
by Yanqing Wen, Baoliang Liu, Haiyan Shi, Shugui Kang and Yuejiao Feng
Axioms 2022, 11(8), 366; https://doi.org/10.3390/axioms11080366 - 27 Jul 2022
Cited by 6 | Viewed by 1560
Abstract
In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive [...] Read more.
In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or k1 consecutive external shocks, the size of at least d1 or k2 consecutive external shocks the size of at least d2 occur, where d1<d2, k1>k2. The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy (L,N). The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Application)
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