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Mathematics
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Stochastic Differential Equations and Their Applications 2020
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Stochastic Differential Equations and Their Applications 2020

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

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 10034

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

18 pages, 672 KiB  
Article
Hyperbolastic Models from a Stochastic Differential Equation Point of View
by Antonio Barrera, Patricia Román-Román and Francisco Torres-Ruiz
Mathematics 2021, 9(16), 1835; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161835 - 04 Aug 2021
Cited by 2 | Viewed by 1438
Abstract
A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of [...] Read more.
A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications 2020)
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7 pages, 249 KiB  
Article
Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control
by Pengju Duan
Mathematics 2021, 9(9), 988; https://0-doi-org.brum.beds.ac.uk/10.3390/math9090988 - 28 Apr 2021
Cited by 3 | Viewed by 1377
Abstract
The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable [...] Read more.
The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications 2020)
22 pages, 1686 KiB  
Article
A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics
by Petras Rupšys, Martynas Narmontas and Edmundas Petrauskas
Mathematics 2020, 8(12), 2230; https://0-doi-org.brum.beds.ac.uk/10.3390/math8122230 - 16 Dec 2020
Cited by 8 | Viewed by 1925
Abstract
The growth and yield modeling of a forest stand has progressed rapidly, starting from the generalized nonlinear regression models of uneven/even-aged stands, and continuing to stochastic differential equation (SDE) models. We focus on the adaptation of the SDEs for the modeling of forest [...] Read more.
The growth and yield modeling of a forest stand has progressed rapidly, starting from the generalized nonlinear regression models of uneven/even-aged stands, and continuing to stochastic differential equation (SDE) models. We focus on the adaptation of the SDEs for the modeling of forest stand dynamics, and relate the tree and stand size variables to the age dimension (time). Two different types of diffusion processes are incorporated into a hybrid model in which the shortcomings of each variable types can be overcome to some extent. This paper presents the hybrid multivariate SDE regarding stand basal area and volume models in a forest stand. We estimate the fixed- and mixed-effect parameters for the multivariate hybrid stochastic differential equation using a maximum likelihood procedure. The results are illustrated using a dataset of measurements from Mountain pine tree (Pinus mugo Turra). Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications 2020)
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21 pages, 2226 KiB  
Article
Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections
by Martynas Narmontas, Petras Rupšys and Edmundas Petrauskas
Mathematics 2020, 8(8), 1363; https://doi.org/10.3390/math8081363 - 14 Aug 2020
Cited by 8 | Viewed by 2136
Abstract
This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are [...] Read more.
This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications 2020)
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16 pages, 1041 KiB  
Article
Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness
by María-Consuelo Casabán, Rafael Company and Lucas Jódar
Mathematics 2020, 8(7), 1112; https://0-doi-org.brum.beds.ac.uk/10.3390/math8071112 - 06 Jul 2020
Cited by 2 | Viewed by 1461
Abstract
In this paper, we propose an integral transform method for the numerical solution of random mean square parabolic models, that makes manageable the computational complexity due to the storage of intermediate information when one applies iterative methods. By applying the random Laplace transform [...] Read more.
In this paper, we propose an integral transform method for the numerical solution of random mean square parabolic models, that makes manageable the computational complexity due to the storage of intermediate information when one applies iterative methods. By applying the random Laplace transform method combined with the use of Monte Carlo and numerical integration of the Laplace transform inversion, an easy expression of the approximating stochastic process allows the manageable computation of the statistical moments of the approximation. Full article
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications 2020)
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