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Mathematics
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Stochastic Differential Equations and Their Applications
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Stochastic Differential Equations and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (15 December 2019) | Viewed by 14889

Special Issue Editor

Prof. Dr. Petras Rupšys

E-Mail Website1 Website2
Guest Editor
Agriculture Academy, Vytautas Magnus University, LT 53361 Kaunas, Lithuania
Interests: numerical and applied mathematics; stochastic differential equations; entropy; mathematical biology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The research area of stochastic differential equations (SDEs) has occupied one of the primary areas of numerical and applied mathematics for the last three decades providing new techniques for analyzing complex systems in mathematical physics, statistical mechanics, finance, biology, medicine, etc., whose evolution is subject to random perturbations. This Special Issue invites original contributions that cover recent advances in the theory and applications of stochastic differential equations. The focus will especially be on articles that examine important applications and those that include detailed case studies.

Potential topics include, but are not limited to:

  • Stochastic differential and partial differential equations (SPDEs)
  • Backward stochastic differential equations
  • Numerical analysis of SDEs and SPDEs
  • Parameter and state estimation of SDEs
  • Random walk in random media
  • Markov processes
  • Stochastic networks
  • Population and evolutionary models
  • Stochastic analysis in finance
  • Stochastic analysis in biology and biomedicine
  • Stochastic differential games
  • Information measures

 

Prof. Dr. Petras Rupšys
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

  • Applied mathematics
  • Stochastic differential equations
  • Mathematical modeling
  • Entropy
  • Mathematical biology

Published Papers (5 papers)

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Research

11 pages, 318 KiB  
Article
Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example
by Ahmed Nafidi, Meriem Bahij, Ramón Gutiérrez-Sánchez and Boujemâa Achchab
Mathematics 2020, 8(2), 160; https://doi.org/10.3390/math8020160 - 23 Jan 2020
Cited by 10 | Viewed by 2456
Abstract
This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits [...] Read more.
This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits and forecasts for a real data set, taking into account the mean value of the process, the maximum likelihood estimators of the parameters of the model and the computational problems that may arise. To carry out the task, we employ the simulated annealing method for finding the estimators values and achieve the study. Finally, to evaluate the capacity of the model, the study is applied to real modeling data where we discuss the accuracy according to error measures. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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20 pages, 1583 KiB  
Article
Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior
by Antonio Barrera, Patricia Román-Román and Francisco Torres-Ruiz
Mathematics 2020, 8(2), 155; https://doi.org/10.3390/math8020155 - 22 Jan 2020
Cited by 3 | Viewed by 3025
Abstract
Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve [...] Read more.
Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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13 pages, 3487 KiB  
Article
A New Approach to Solving Stochastic Optimal Control Problems
by Pablo T. Rodriguez-Gonzalez, Vicente Rico-Ramirez, Ramiro Rico-Martinez and Urmila M. Diwekar
Mathematics 2019, 7(12), 1207; https://doi.org/10.3390/math7121207 - 09 Dec 2019
Cited by 10 | Viewed by 2988
Abstract
A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from [...] Read more.
A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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21 pages, 1121 KiB  
Article
Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness
by M. Consuelo Casabán, Rafael Company and Lucas Jódar
Mathematics 2019, 7(9), 853; https://doi.org/10.3390/math7090853 - 16 Sep 2019
Cited by 3 | Viewed by 2007
Abstract
This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random [...] Read more.
This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method. The recovery of the solution of the original random partial differential problem throughout the inverse integral transform allows its numerical approximation using Gaussian quadratures involving the evaluation of the solution of the random ordinary differential problem at certain concrete values, which are approximated using Monte Carlo method. Numerical experiments illustrating the numerical convergence of the method are included. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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22 pages, 5959 KiB  
Article
Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures
by Petras Rupšys
Mathematics 2019, 7(8), 761; https://doi.org/10.3390/math7080761 - 19 Aug 2019
Cited by 13 | Viewed by 2631
Abstract
This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a [...] Read more.
This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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