Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps
Numerical approximation is a vital method to investigate the properties of stochastic age-dependent population systems, since most stochastic age-dependent population systems cannot be solved explicitly. In this paper, a Taylor approximation scheme for a class of age-dependent stochastic delay popul...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-03-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020145?viewType=HTML |
| id |
doaj-0b5e30fd8a484a7b9719624e0ea628cc |
|---|---|
| record_format |
Article |
| spelling |
doaj-0b5e30fd8a484a7b9719624e0ea628cc2021-07-22T02:02:15ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-03-011732650267510.3934/mbe.2020145Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumpsWenrui Li0Qimin Zhang1Meyer-Baese Anke2Ming Ye3Yan Li 41. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China2. Department of Scientific Computing, Florida State University, Tallahassee FL 32306-4120, USA3. Department of Earth, Ocean, and Atmospheric Science and Department of Scientific Computing, Florida State University, Tallahassee FL 32306, USA1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, ChinaNumerical approximation is a vital method to investigate the properties of stochastic age-dependent population systems, since most stochastic age-dependent population systems cannot be solved explicitly. In this paper, a Taylor approximation scheme for a class of age-dependent stochastic delay population equations with mean-reverting Ornstein-Uhlenbeck (OU) process and Poisson jumps is presented. In case that the coefficients of drift and diffusion are Taylor approximations, we prove that the numerical solutions converge to the exact solutions for these equations. Moreover, the convergence order of the numerical scheme is given. Finally, some numerical simulations are discussed to illustrate the theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2020145?viewType=HTMLstochastic age-dependent population equationstime delayornstein-uhlenbeck processtaylor approximation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wenrui Li Qimin Zhang Meyer-Baese Anke Ming Ye Yan Li |
| spellingShingle |
Wenrui Li Qimin Zhang Meyer-Baese Anke Ming Ye Yan Li Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps Mathematical Biosciences and Engineering stochastic age-dependent population equations time delay ornstein-uhlenbeck process taylor approximation |
| author_facet |
Wenrui Li Qimin Zhang Meyer-Baese Anke Ming Ye Yan Li |
| author_sort |
Wenrui Li |
| title |
Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps |
| title_short |
Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps |
| title_full |
Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps |
| title_fullStr |
Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps |
| title_full_unstemmed |
Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps |
| title_sort |
taylor approximation of the solution of age-dependent stochastic delay population equations with ornstein-uhlenbeck process and poisson jumps |
| publisher |
AIMS Press |
| series |
Mathematical Biosciences and Engineering |
| issn |
1551-0018 |
| publishDate |
2020-03-01 |
| description |
Numerical approximation is a vital method to investigate the properties of stochastic age-dependent population systems, since most stochastic age-dependent population systems cannot be solved explicitly. In this paper, a Taylor approximation scheme for a class of age-dependent stochastic delay population equations with mean-reverting Ornstein-Uhlenbeck (OU) process and Poisson jumps is presented. In case that the coefficients of drift and diffusion are Taylor approximations, we prove that the numerical solutions converge to the exact solutions for these equations. Moreover, the convergence order of the numerical scheme is given. Finally, some numerical simulations are discussed to illustrate the theoretical results. |
| topic |
stochastic age-dependent population equations time delay ornstein-uhlenbeck process taylor approximation |
| url |
https://www.aimspress.com/article/doi/10.3934/mbe.2020145?viewType=HTML |
| work_keys_str_mv |
AT wenruili taylorapproximationofthesolutionofagedependentstochasticdelaypopulationequationswithornsteinuhlenbeckprocessandpoissonjumps AT qiminzhang taylorapproximationofthesolutionofagedependentstochasticdelaypopulationequationswithornsteinuhlenbeckprocessandpoissonjumps AT meyerbaeseanke taylorapproximationofthesolutionofagedependentstochasticdelaypopulationequationswithornsteinuhlenbeckprocessandpoissonjumps AT mingye taylorapproximationofthesolutionofagedependentstochasticdelaypopulationequationswithornsteinuhlenbeckprocessandpoissonjumps AT yanli taylorapproximationofthesolutionofagedependentstochasticdelaypopulationequationswithornsteinuhlenbeckprocessandpoissonjumps |
| _version_ |
1721292254762500096 |