Special Issue "Stochastic Statistics and Modeling"

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

Deadline for manuscript submissions: closed (1 March 2021).

Special Issue Editors

Prof. Dr. Patricia Román-Román
E-Mail Website
Guest Editor
Department of Statistics and Operations Research, Faculty of Sciences, s/n, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
Interests: Stochastic modeling by diffusion processes; inference in diffusion processes; first-passage-times; tumor growth modeling.
Prof. Dr. María Jesús García-Ligero
E-Mail Website
Guest Editor
Department of Statistics and Operations Research, Faculty of Sciences, s/n, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
Interests: Stochastic systems; dynamical modeling; signal processing; signal control and estimation.

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics will publish original research papers that cover the study of several topics related to the stochastic modeling of dynamical systems. The focus will be the introduction and study of new dynamic models that can model phenomena in areas of application. Contributions considering the study of existing models will also be welcome (inference, applications in real phenomena, resolution of problems related to the type of phenomenon under study, etc.)

Potential topics include:

  • Modeling by stochastic processes
  • Inference in stochastic processes
  • First-passage-times
  • Computational methods for stochastic processes
  • Dynamical systems estimation
  • Signal processing
  • Filtering and smoothing algorithms
  • Applications in risk theory, insurance and mathematical finance, biosciences and environmental science, cell proliferation, and other areas of interest.

Prof. Dr. Patricia Román-Román
Prof. Dr. María Jesús García-Ligero
Guest Editors

Manuscript Submission Information

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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 1600 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 modeling by dynamical systems
  • Signal processing
  • Inference in stochastic processes
  • Filtering and smoothing
  • First-passage-times

Published Papers (9 papers)

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Research

Article
T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms
Mathematics 2021, 9(9), 959; https://doi.org/10.3390/math9090959 - 25 Apr 2021
Viewed by 393
Abstract
The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a [...] Read more.
The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes
Mathematics 2021, 9(8), 818; https://doi.org/10.3390/math9080818 - 09 Apr 2021
Cited by 1 | Viewed by 403
Abstract
General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance [...] Read more.
General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance are included in the considered class. For these processes, the transition probability density function is explicitly determined. Moreover, simulation procedures are applied to the diffusion processes obtained starting from Wiener and Ornstein–Uhlenbeck processes. Specific examples in which the infinitesimal moments include periodic functions are discussed. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Using First-Passage Times to Analyze Tumor Growth Delay
Mathematics 2021, 9(6), 642; https://doi.org/10.3390/math9060642 - 17 Mar 2021
Viewed by 411
Abstract
A central aspect of in vivo experiments with anticancer therapies is the comparison of the effect of different therapies, or doses of the same therapeutic agent, on tumor growth. One of the most popular clinical endpoints is tumor growth delay, which measures the [...] Read more.
A central aspect of in vivo experiments with anticancer therapies is the comparison of the effect of different therapies, or doses of the same therapeutic agent, on tumor growth. One of the most popular clinical endpoints is tumor growth delay, which measures the effect of treatment on the time required for tumor volume to reach a specific value. This effect has been analyzed through a variety of statistical methods: conventional descriptive analysis, linear regression, Cox regression, etc. We propose a new approach based on stochastic modeling of tumor growth and the study of first-passage time variables. This approach allows us to prove that the time required for tumor volume to reach a specific value must be determined empirically as the average of the times required for the volume of individual tumors to reach said value instead of the time required for the average volume of the tumors to reach the value of interest. In addition, we define several measures in random environments to compare the time required for the tumor volume to multiply k times its initial volume in control, as well as treated groups, and the usefulness of these measures is illustrated by means of an application to real data. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Demographic Dynamics in Multitype Populations with Migrations
Mathematics 2021, 9(3), 246; https://doi.org/10.3390/math9030246 - 27 Jan 2021
Viewed by 422
Abstract
This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type [...] Read more.
This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility
Mathematics 2021, 9(2), 126; https://doi.org/10.3390/math9020126 - 08 Jan 2021
Viewed by 634
Abstract
Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps [...] Read more.
Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Estimating General Parameters from Non-Probability Surveys Using Propensity Score Adjustment
Mathematics 2020, 8(11), 2096; https://doi.org/10.3390/math8112096 - 23 Nov 2020
Cited by 1 | Viewed by 606
Abstract
This study introduces a general framework on inference for a general parameter using nonprobability survey data when a probability sample with auxiliary variables, common to both samples, is available. The proposed framework covers parameters from inequality measures and distribution function estimates but the [...] Read more.
This study introduces a general framework on inference for a general parameter using nonprobability survey data when a probability sample with auxiliary variables, common to both samples, is available. The proposed framework covers parameters from inequality measures and distribution function estimates but the scope of the paper is broader. We develop a rigorous framework for general parameter estimation by solving survey weighted estimating equations which involve propensity score estimation for units in the non-probability sample. This development includes the expression of the variance estimator, as well as some alternatives which are discussed under the proposed framework. We carried a simulation study using data from a real-world survey, on which the application of the estimation methods showed the effectiveness of the proposed design-based inference on several general parameters. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
Article
New Modeling Approaches Based on Varimax Rotation of Functional Principal Components
Mathematics 2020, 8(11), 2085; https://doi.org/10.3390/math8112085 - 22 Nov 2020
Cited by 5 | Viewed by 1111
Abstract
Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of [...] Read more.
Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays
Mathematics 2020, 8(11), 1948; https://doi.org/10.3390/math8111948 - 04 Nov 2020
Cited by 1 | Viewed by 505
Abstract
This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the [...] Read more.
This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the signal, and delays may occur during transmission. These uncertainties are commonly described by means of independent Bernoulli random variables. In the present paper, the model is generalised in two directions: (i) at each sensor, the degradation in the measurements is modelled by sequences of random variables with arbitrary distribution over the interval [0, 1]; (ii) transmission delays are described using three-state homogeneous Markov chains (Markovian delays), thus modelling dependence at different sampling times. Assuming that the measurement noises are correlated and cross-correlated at both simultaneous and consecutive sampling times, and that the evolution of the signal process is unknown, we address the problem of signal estimation in terms of covariances, using the following distributed fusion method. First, the local filtering and fixed-point smoothing algorithms are obtained by an innovation approach. Then, the corresponding distributed fusion estimators are obtained as a matrix-weighted linear combination of the local ones, using the mean squared error as the criterion of optimality. Finally, the efficiency of the algorithms obtained, measured by estimation error covariance matrices, is shown by a numerical simulation example. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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Article
Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model
Mathematics 2020, 8(10), 1638; https://doi.org/10.3390/math8101638 - 23 Sep 2020
Cited by 2 | Viewed by 622
Abstract
Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim [...] Read more.
Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim sizes of sample. However, whether the estimators are asymptotically normal or not is unknown. In this paper, we give the details to verify the asymptotic normality of these estimators and present some simulation examples to support our result. Full article
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
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