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STABILITY ANALYSIS AND PARAMETER ESTIMATION OF A STOCHASTIC LOGISTIC GROWTH MODEL WITH MULTIPLICATIVE α-STABLE LÉVY NOISE
| Title: | STABILITY ANALYSIS AND PARAMETER ESTIMATION OF A STOCHASTIC LOGISTIC GROWTH MODEL WITH MULTIPLICATIVE α-STABLE LÉVY NOISE. |
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| Name(s): |
Bhusal, Bikram , author Long, Hongwei , Thesis advisor Florida Atlantic University, Degree grantor Department of Mathematical Sciences Charles E. Schmidt College of Science |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2022 | |
| Date Issued: | 2022 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 95 p. | |
| Language(s): | English | |
| Abstract/Description: | Since the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations(SDEs) that are driven not only by Brownian motion but also by α-stable Lévy noises are more appropriate to model such statistical behavior of non-Gaussian processes with heavy-tailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes defined as solutions to stochastic logistic differential equations driven by multiplicative α-stable Lévy noise. We mainly focus on one-dimensional stochastic logistic jump-diffusion processes driven by Brownian motion and α-stable Lévy motion. First, we present the stability analysis of the solution of a stochastic logistic growth model with multiplicative α-stable Lévy. We establish the existence of a unique global positive solution of this model under certain conditions. Then, we find the sufficient conditions for the almost sure exponential stability of the trivial solution of the model. Next, we provide parameter estimation for the proposed model. In parameter estimation, we use statistical methods to get an optimal and applicable estimator. We also investigate the consistency and asymptotics of the proposed estimator. We assess the validity of the estimators with a simulation study. | |
| Identifier: | FA00014043 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2022. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Parameter estimation Stochastic processes Lévy processes |
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| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00014043 | |
| Use and Reproduction: | Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
