Stochastic Processes: Theory, Simulation and Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 723

Special Issue Editors


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Guest Editor
Department of Mathematics, University of Salerno, I-84100 Salerno, Italy
Interests: stochastic processes; applied probability; probability theory; stochastic models
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Guest Editor
Dipartimento di Informatica/DI, University of Salerno, I-84100 Salerno, Italy
Interests: diffusion processes for growth phenomena; theoretical studies on Markov and Gaussian processes; models to describe neuronal systems; first-passage-times
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to this Special Issue of Mathematics, which is dedicated to presenting innovative results.

Contributions on the theory and simulation of stochastic processes and their applications are especially welcome. The focus is also oriented toward, but not limited to, the design and analysis of probabilistic models, Markov and Gaussian stochastic processes, computational methods, first-passage-time problems, and applications to biomathematical modeling, reliability theory, risk theory and queueing systems. Attention is also given to problems of both a theoretical and computational nature related to the following themes: 

  • Probabilistic models for neuronal systems;
  • Adaptive service systems;
  • Population growth models in random environments;
  • Algorithms for the evaluation of first-crossing probability densities through suitable boundaries;
  • Asymptotic behaviors of probability densities for Markov and Gauss processes.

Prof. Dr. Antonio Di Crescenzo
Prof. Virginia Giorno
Guest Editors

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Keywords

  • birth–death processes
  • computational methods for stochastic models
  • diffusion processes
  • first-passage-time problems
  • Gauss–Markov processes
  • Markov chains
  • neuronal modeling
  • population dynamics
  • probability theory
  • queueing systems
  • random walks
  • simulation of stochastic processes
  • stochastic models in biology
  • stochastic processes and applications
  • finite-velocity random motions
  • reliability theory
  • risk theory
  • stochastic methods for machine learning
  • stochastic processes governed by fractional equations

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Published Papers (1 paper)

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Research

22 pages, 524 KB  
Article
General Markov Chains: Dimension of the Space of Invariant Finitely Additive Measures and Their Ergodicity—Problematic Examples
by Alexander Zhdanok
Mathematics 2025, 13(22), 3690; https://doi.org/10.3390/math13223690 - 17 Nov 2025
Viewed by 207
Abstract
This study considers general Markov chains (MCs) with discrete time in an arbitrary phase space. The transition function of the MC generates two operators: T, which acts on the space of measurable functions, and A, which acts on the space of [...] Read more.
This study considers general Markov chains (MCs) with discrete time in an arbitrary phase space. The transition function of the MC generates two operators: T, which acts on the space of measurable functions, and A, which acts on the space of bounded countably additive measures. The operator T*, which is adjoint to T and acts on the space of finitely additive measures, is also constructed. A number of theorems are proved for the operator T*, including the ergodic theorem. Under certain conditions it is proved that if the MC has a finite number of basic invariant finitely additive measures then all of them are countably additive and the MC is quasi-compact. We demonstrate a methodology that applies finitely additive measures for the analysis of MCs, using examples with detailed proofs of their non-simple properties. Some of these proofs in the examples are more complicated than the proofs in our theorems. Full article
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