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Mathematics
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Advanced Stochastic Modelling and Applications
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Advanced Stochastic Modelling and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 4366

Special Issue Editor

Dr. Song-Kyoo (Amang) Kim

E-Mail Website
Guest Editor
Faculty of Applied Sciences, Macao Polytechnic University, Macau, China
Interests: stochastic models; probability theory; stochastic duel game; blockchain governance game; innovations and technologies
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We would like to invite you to submit your work to the Special Issue “Advanced Stochastic Modelling and Applications”, which aligns with stochastic/uncertainty phenomena. This Special Issue seeks high-quality contributions in both theoretical and applied stochastic modelling used to solve real-world problems and issues.

Dr. Song-Kyoo (Amang) Kim
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • probability theory
  • stochastic models
  • game theoretic analysis of stochastic models
  • novel queueing models in applications
  • multidimensional Markov chains
  • operations research
  • stochastic analysis of machine learning systems

Published Papers (4 papers)

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Research

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14 pages, 3384 KiB  
Article
Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger
by Irina Bashkirtseva, Makar Pavletsov, Tatyana Perevalova and Lev Ryashko
Mathematics 2023, 11(20), 4302; https://doi.org/10.3390/math11204302 - 16 Oct 2023
Viewed by 731
Abstract
Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dynamic interaction of reagent [...] Read more.
Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dynamic interaction of reagent concentration and temperature in autocatalysis. For the deterministic variant of this model, mono- and bistability parameter zones as well as local and global bifurcations are revealed, and we show how random multiplicative disturbances can deform coexisting equilibrium regimes. In a study of noise-induced transitions, we apply direct numerical simulation and an analytical approach based on the stochastic sensitivity technique. Two variants of bistability with different scenarios of stochastic transformations are studied and compared. Full article
(This article belongs to the Special Issue Advanced Stochastic Modelling and Applications)
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27 pages, 633 KiB  
Article
Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information
by Jewgeni H. Dshalalow and Hend Aljahani
Mathematics 2023, 11(16), 3568; https://doi.org/10.3390/math11163568 - 17 Aug 2023
Cited by 1 | Viewed by 663
Abstract
We study a reliability system subject to occasional random shocks of random magnitudes W0,W1,W2,… occurring at times τ0,τ1,τ2,…. Any such shock is harmless or [...] Read more.
We study a reliability system subject to occasional random shocks of random magnitudes W0,W1,W2,… occurring at times τ0,τ1,τ2,…. Any such shock is harmless or critical dependent on Wk≤H or Wk>H, given a fixed threshold H. It takes a total of N critical shocks to knock the system down. In addition, the system ages in accordance with a monotone increasing continuous function δ, so that when δT crosses some sustainability threshold D at time T, the system becomes essentially inoperational. However, it can still function for a while undetected. The most common way to do the checking is at one of the moments τ1,τ2,… when the shocks are registered. Thus, if crossing of D by δ occurs at time T∈τk,τk+1, only at time τk+1, can one identify the system’s failure. The age-related failure is detected with some random delay. The objective is to predict when the system fails, through the Nth critical shock or by the observed aging moment, whichever of the two events comes first. We use and embellish tools of discrete and continuous operational calculus (D-operator and Laplace–Carson transform), combined with first-passage time analysis of random walk processes, to arrive at fully explicit functionals of joint distributions for the observed lifetime of the system and cumulative damage to the system. We discuss various special cases and modifications including the assumption that D is random (and so is T). A number of examples and numerically drawn figures demonstrate the analytic tractability of the results. Full article
(This article belongs to the Special Issue Advanced Stochastic Modelling and Applications)
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20 pages, 716 KiB  
Article
Dynamic Output Feedback Quantization Control of a Networked Control System with Dual-Channel Data Packet Loss
by Fan Zhang, Mingang Hua and Mengyu Gao
Mathematics 2023, 11(11), 2544; https://doi.org/10.3390/math11112544 - 1 Jun 2023
Viewed by 1031
Abstract
In this paper, the design of a dynamic output feedback controller for a networked control system with dual-channel data packet loss and special discrete-time delay is studied, in which the data packet loss is described by the Markov process. In order to effectively [...] Read more.
In this paper, the design of a dynamic output feedback controller for a networked control system with dual-channel data packet loss and special discrete-time delay is studied, in which the data packet loss is described by the Markov process. In order to effectively alleviate the problem of network congestion, a quantizer was added to the sensor-to-controller channel. The transition probabilities of the Markov process are uncertain, but they exist in the convex sets of known convex polyhedron types. The mode-dependent Lyapunov function was constructed, and a sufficient condition was given to make the closed-loop system stochastically stable and satisfy the performance index. The parameters of the controller were solved by the linear matrix inequality method. Finally, an example of aircraft shows the validity of the proposed approach. A numerical example is compared with other literature, showing the superiority of the proposed approach. Full article
(This article belongs to the Special Issue Advanced Stochastic Modelling and Applications)
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Review

Jump to: Research

21 pages, 1091 KiB  
Review
Various Blockchain Governance Games: A Review
by Song-Kyoo (Amang) Kim
Mathematics 2023, 11(10), 2273; https://doi.org/10.3390/math11102273 - 12 May 2023
Cited by 1 | Viewed by 1198
Abstract
Blockchain Governance Game (BGG) is the stochastic model for describing the innovative security enhancement of decentralized network architectures. This hybrid model provides the best strategies to prepare for preventing network failures by attackers. Strategic alliance for the Blockchain Governance Game, a successor to [...] Read more.
Blockchain Governance Game (BGG) is the stochastic model for describing the innovative security enhancement of decentralized network architectures. This hybrid model provides the best strategies to prepare for preventing network failures by attackers. Strategic alliance for the Blockchain Governance Game, a successor to BGG, adds the strategic alliance to prevent attacks by adapting the concept from business domains. The multi-layered Blockchain Governance Game was developed by combining these two basic models to defend complex networks. This paper not only provides a brief summary of each game model, but also identifies two key network security applications based on BGGs that could serve as a guide for actual implementation. This review is intended to encourage people to be inspired for their future research. The author hopes to encourage readers working in related research areas who might integrate BGG models into their research. Full article
(This article belongs to the Special Issue Advanced Stochastic Modelling and Applications)
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