Stochastic Modeling and Its Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 29 August 2024 | Viewed by 1677

Special Issue Editors


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Guest Editor
Insitute of Systems Science, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Interests: stochastic process; modeling and dynamical analyses of biological systems and infectious systems; computer simulation
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Interests: stochastic differential equations and their applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original research articles covering advances in the theory of stochastic modeling in phenomena arising from the real world. In this framework, stochastic continuous and discrete time processes will be discussed, as will stochastic optimal controls and computer simulation techniques. All of the above topics are intended to be treated in the spirit of modeling the evolution of stochastic systems of interest in biology, infectious diseases, economics, and other related research fields.

Potential topics include, but are not limited to, the following:

  • Stochastic processes for economic activity;
  • Stochastic models and analyses for biological systems;
  • Stochastic models and analyses applied to epidemiology;
  • Stochastic computational biology;
  • Stochastic optimal control for biological systems;
  • Parameter estimation and sensitivity analyses of stochastic biological systems. 

Prof. Dr. Chao Liu
Dr. Qun Liu
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 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 process
  • stochastic persistence in mean
  • ergodicity
  • uniqueness and existence of global positive solutions
  • optimal control

Published Papers (2 papers)

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Research

31 pages, 392 KiB  
Article
One-Dimensional BSDEs with Jumps and Logarithmic Growth
by El Mountasar Billah Bouhadjar, Nabil Khelfallah and Mhamed Eddahbi
Axioms 2024, 13(6), 354; https://doi.org/10.3390/axioms13060354 - 24 May 2024
Viewed by 374
Abstract
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with [...] Read more.
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with respect to the jump component. Our study rigorously establishes the existence and uniqueness of solutions within suitable functional spaces. Additionally, we relax the Lipschitz condition on the Poisson component, permitting the generator to exhibit logarithmic growth with respect to all variables. Taking a step further, we employ an exponential transformation to establish an equivalence between a solution of a BSDEJ exhibiting quadratic growth in the z-variable and a BSDEJ showing a logarithmic growth with respect to y and z. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
25 pages, 399 KiB  
Article
Malliavin Regularity of Non-Markovian Quadratic BSDEs and Their Numerical Schemes
by Salima Doubbakh, Nabil Khelfallah, Mhamed Eddahbi and Anwar Almualim
Axioms 2023, 12(4), 366; https://doi.org/10.3390/axioms12040366 - 10 Apr 2023
Viewed by 888
Abstract
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic differential equations (QBSDEs for short) in cases where the terminal data need not be a function of a forward diffusion. By using the connection between the QBSDE [...] Read more.
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic differential equations (QBSDEs for short) in cases where the terminal data need not be a function of a forward diffusion. By using the connection between the QBSDE under study and some backward stochastic differential equations (BSDEs) with global Lipschitz coefficients, we firstly prove Lq, (q2) existence and uniqueness results for QBSDE. Secondly, the Lp-Hölder continuity of the solutions is established for (q>4 and 2p<q2). Then, we analyze some numerical schemes for our systems and establish their rates of convergence. Moreover, our results are illustrated with three examples. Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
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