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Probabilistic Models for Dynamical Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (1 December 2024) | Viewed by 3699

Special Issue Editor


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Guest Editor
Signal Processing Lab, Department of Electrical and Computer Engineering, University of São Paulo, São Carlos 13566-590, Brazil
Interests: dynamic system modeling; probabilistic models; network models; dynamic Bayesian network; complex system models

Special Issue Information

Dear Colleagues,

Probabilistic models employed in the analysis of dynamical systems involve the incorporation of stochastic components inside variables and time-varying systems. These models have the capability to simulate nonlinear and stochastic dynamic models, thus facilitating the examination of their applicability in many areas. Moreover, they are employed in the creation of innovative, dynamic models, which encompass structures that vary over time, as well as in the continuous monitoring of dynamic systems. Probabilistic models are widely utilised in several areas, such as engineering disciplines, robotics, finance, and medical research. Probabilistic models can also be used to estimate the probability of future events or states based on past observations, making them useful in predicting the behaviour of complex systems, such as weather patterns or financial markets. Other methods for probabilistic modelling of dynamical systems include Gaussian processes, Bayesian inference, Monte Carlo simulations, Markov processes using imperfect probability and the incorporation of partially observable variables. The use of probabilistic models can also have ethical implications, particularly in fields such as autonomous vehicles and medical diagnosis. Ongoing research in the field of probabilistic modelling is focused on developing more efficient algorithms and techniques for handling high-dimensional problems, as well as improving the accuracy and interpretability of these models. The practical implementation of probabilistic models for dynamical systems is faced with numerous challenges, including high dimensionality, complex model structures, limited data availability, computationally intensive procedures, model selection, and the existence of uncertainty in data and models.

Dr. Carlos Dias Maciel
Guest Editor

Manuscript Submission Information

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Keywords

  • dynamic system modeling
  • probabilistic models
  • network models
  • dynamic Bayesian network
  • complex system models

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Published Papers (3 papers)

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Research

21 pages, 389 KiB  
Article
Distribution Approach to Local Volatility for European Options in the Merton Model with Stochastic Interest Rates
by Piotr Nowak and Dariusz Gatarek
Entropy 2025, 27(3), 320; https://doi.org/10.3390/e27030320 - 19 Mar 2025
Viewed by 296
Abstract
The Dupire formula is a very useful tool for pricing financial derivatives. This paper is dedicated to deriving the aforementioned formula for the European call option in the space of distributions by applying a mathematically rigorous approach developed in our previous paper concerning [...] Read more.
The Dupire formula is a very useful tool for pricing financial derivatives. This paper is dedicated to deriving the aforementioned formula for the European call option in the space of distributions by applying a mathematically rigorous approach developed in our previous paper concerning the case of the Margrabe option. We assume that the underlying asset is described by the Merton jump-diffusion model. Using this stochastic process allows us to take into account jumps in the price of the considered asset. Moreover, we assume that the instantaneous interest rate follows the Merton model (1973). Therefore, in contrast to the models combining a constant interest rate and a continuous underlying asset price process, frequently observed in the literature, applying both stochastic processes could accurately reflect financial market behaviour. Moreover, we illustrate the possibility of using the minimal entropy martingale measure as the risk-neutral measure in our approach. Full article
(This article belongs to the Special Issue Probabilistic Models for Dynamical Systems)
22 pages, 2677 KiB  
Article
Assessing Credibility in Bayesian Networks Structure Learning
by Vitor Barth, Fábio Serrão and Carlos Maciel
Entropy 2024, 26(10), 829; https://doi.org/10.3390/e26100829 - 30 Sep 2024
Viewed by 997
Abstract
Learning Bayesian networks from data aims to create a Directed Acyclic Graph that encodes significant statistical relationships between variables and their joint probability distributions. However, when using real-world data with limited knowledge of the original dynamical system, it is challenging to determine if [...] Read more.
Learning Bayesian networks from data aims to create a Directed Acyclic Graph that encodes significant statistical relationships between variables and their joint probability distributions. However, when using real-world data with limited knowledge of the original dynamical system, it is challenging to determine if the learned DAG accurately reflects the underlying relationships, especially when the data come from multiple independent sources. This paper describes a methodology capable of assessing the credible interval for the existence and direction of each edge within Bayesian networks learned from data, without previous knowledge of the underlying dynamical system. It offers several advantages over classical methods, such as data fusion from multiple sources, identification of latent variables, and extraction of the most prominent edges with their respective credible interval. The method is evaluated using simulated datasets of various sizes and a real use case. Our approach was verified to achieve results comparable to the most recent studies in the field, while providing more information on the model’s credibility. Full article
(This article belongs to the Special Issue Probabilistic Models for Dynamical Systems)
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23 pages, 2002 KiB  
Article
Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling
by Taketo Omi and Toshiaki Omori
Entropy 2024, 26(8), 653; https://doi.org/10.3390/e26080653 - 30 Jul 2024
Viewed by 1415
Abstract
Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only [...] Read more.
Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems. Full article
(This article belongs to the Special Issue Probabilistic Models for Dynamical Systems)
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