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Mathematics
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Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis
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Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis

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

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 20397

Special Issue Editors

Prof. Dr. Virginia Giorno

E-Mail Website
Guest Editor
Dipartimento di Informatica/DI, University of Salerno, 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
Prof. Dr. Francisco De Asís Torres-Ruiz

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: diffusion processes for growth phenomena; inference in diffusion processes; first-passage-times; model selection
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The main aim of this Special Issue of Mathematics is to publish original research papers that cover the study of several topics related to diffusion processes. The focus will especially be on the study of diffusion processes that model dynamic phenomena governed by growth curves, including the modification of existing ones by incorporating additional information to the one proposed by the dynamic variable under study. Both the probabilistic study of the introduced models and the applications to research areas are welcome. Among the fields of application, we can mention biology, economics, medicine, energy, etc. The inference in the considered processes will be another of the points of interest of this issue, including the use and ad hoc adaptation of stochastic and metaheuristic optimization procedures.

Potential topics include:

  • stochastic biological models
  • sigmoidal growth curves
  • computational methods for diffusion processes
  • inference in diffusion processes
  • first-passage-times
  • applications in risk theory, insurance, and mathematical finance
  • applications in biosciences and environmental sciences
  • applications in cell proliferation

Prof. Virginia Giorno
Prof. Francisco de Asís Torres-Ruiz
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 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

  • dynamic growth phenomena
  • inference in diffusion processes
  • numerical methods for diffusion processes
  • applications of diffusion processes

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Published Papers (5 papers)

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Research

14 pages, 646 KiB  
Article
A Class of Itô Diffusions with Known Terminal Value and Specified Optimal Barrier
by Bernardo D’Auria and Alessandro Ferriero
Mathematics 2020, 8(1), 123; https://doi.org/10.3390/math8010123 - 14 Jan 2020
Cited by 1 | Viewed by 2120
Abstract
In this paper, we study the optimal stopping-time problems related to a class of Itô diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the [...] Read more.
In this paper, we study the optimal stopping-time problems related to a class of Itô diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explicit solution to these optimization problems and in particular we provide a class of processes whose optimal barrier has the same form as the one of the Brownian bridge. These processes may be a possible alternative to the Brownian bridge in practice as they could better model real applications. Moreover, we discuss the existence of a process with a prescribed curve as optimal barrier, for any given (decreasing) curve. This gives a modeling approach for the optimal liquidation time, i.e., the optimal time at which the investor should liquidate a position to maximize the gain. Full article
(This article belongs to the Special Issue Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis)
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24 pages, 860 KiB  
Article
On the Construction of Some Fractional Stochastic Gompertz Models
by Giacomo Ascione and Enrica Pirozzi
Mathematics 2020, 8(1), 60; https://doi.org/10.3390/math8010060 - 2 Jan 2020
Cited by 9 | Viewed by 2387
Abstract
The aim of this paper is the construction of stochastic versions for some fractional Gompertz curves. To do this, we first study a class of linear fractional-integral stochastic equations, proving existence and uniqueness of a Gaussian solution. Such kinds of equations are then [...] Read more.
The aim of this paper is the construction of stochastic versions for some fractional Gompertz curves. To do this, we first study a class of linear fractional-integral stochastic equations, proving existence and uniqueness of a Gaussian solution. Such kinds of equations are then used to construct fractional stochastic Gompertz models. Finally, a new fractional Gompertz model, based on the previous two, is introduced and a stochastic version of it is provided. Full article
(This article belongs to the Special Issue Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis)
19 pages, 988 KiB  
Article
Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions
by Virginia Giorno and Amelia G. Nobile
Mathematics 2019, 7(6), 555; https://doi.org/10.3390/math7060555 - 18 Jun 2019
Cited by 10 | Viewed by 3153
Abstract
We consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise intensity, whose conditional median coincides with the deterministic solution. [...] Read more.
We consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise intensity, whose conditional median coincides with the deterministic solution. The second is a shifted-restricted Gompertz-type diffusion process with a reflecting condition in zero state and with time-dependent regulation functions. For both processes, we analyze the transient and the asymptotic behavior of the transition probability density functions and their conditional moments. Particular attention is dedicated to the first-passage time, by deriving some closed form for its density through special boundaries. Finally, special cases of periodic regulation functions are discussed. Full article
(This article belongs to the Special Issue Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis)
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18 pages, 1146 KiB  
Article
A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise
by Patricia Román-Román, Juan José Serrano-Pérez and Francisco Torres-Ruiz
Mathematics 2019, 7(6), 541; https://doi.org/10.3390/math7060541 - 13 Jun 2019
Cited by 15 | Viewed by 4218
Abstract
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve [...] Read more.
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented. Full article
(This article belongs to the Special Issue Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis)
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28 pages, 598 KiB  
Article
Logistic Growth Described by Birth-Death and Diffusion Processes
by Antonio Di Crescenzo and Paola Paraggio
Mathematics 2019, 7(6), 489; https://doi.org/10.3390/math7060489 - 28 May 2019
Cited by 20 | Viewed by 7884
Abstract
We consider the logistic growth model and analyze its relevant properties, such as the limits, the monotony, the concavity, the inflection point, the maximum specific growth rate, the lag time, and the threshold crossing time problem. We also perform a comparison with other [...] Read more.
We consider the logistic growth model and analyze its relevant properties, such as the limits, the monotony, the concavity, the inflection point, the maximum specific growth rate, the lag time, and the threshold crossing time problem. We also perform a comparison with other growth models, such as the Gompertz, Korf, and modified Korf models. Moreover, we focus on some stochastic counterparts of the logistic model. First, we study a time-inhomogeneous linear birth-death process whose conditional mean satisfies an equation of the same form of the logistic one. We also find a sufficient and necessary condition in order to have a logistic mean even in the presence of an absorbing endpoint. Then, we obtain and analyze similar properties for a simple birth process, too. Then, we investigate useful strategies to obtain two time-homogeneous diffusion processes as the limit of discrete processes governed by stochastic difference equations that approximate the logistic one. We also discuss an interpretation of such processes as diffusion in a suitable potential. In addition, we study also a diffusion process whose conditional mean is a logistic curve. In more detail, for the considered processes we study the conditional moments, certain indices of dispersion, the first-passage-time problem, and some comparisons among the processes. Full article
(This article belongs to the Special Issue Diffusion Processes Associated with Growth Curves: Probabilistic and Inferential Analysis)
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