A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics
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 dynam...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2230 |
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| author | Petras Rupšys Martynas Narmontas Edmundas Petrauskas |
| author_facet | Petras Rupšys Martynas Narmontas Edmundas Petrauskas |
| author_sort | Petras Rupšys |
| collection | DOAJ |
| description | 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 (<i>Pinus mugo</i> Turra). |
| first_indexed | 2024-03-10T14:01:47Z |
| format | Article |
| id | doaj.art-2a95dd8c12914c90b27bc82b3736d7a5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:01:47Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2a95dd8c12914c90b27bc82b3736d7a52023-11-21T01:03:23ZengMDPI AGMathematics2227-73902020-12-01812223010.3390/math8122230A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand DynamicsPetras Rupšys0Martynas Narmontas1Edmundas Petrauskas2Agriculture Academy, Vytautas Magnus University, 53361 Kaunas, LithuaniaAgriculture Academy, Vytautas Magnus University, 53361 Kaunas, LithuaniaAgriculture Academy, Vytautas Magnus University, 53361 Kaunas, LithuaniaThe 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 (<i>Pinus mugo</i> Turra).https://www.mdpi.com/2227-7390/8/12/2230stochastic differential equationprobability density functionstand basal areastand volumequantiles |
| spellingShingle | Petras Rupšys Martynas Narmontas Edmundas Petrauskas A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics Mathematics stochastic differential equation probability density function stand basal area stand volume quantiles |
| title | A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics |
| title_full | A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics |
| title_fullStr | A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics |
| title_full_unstemmed | A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics |
| title_short | A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics |
| title_sort | multivariate hybrid stochastic differential equation model for whole stand dynamics |
| topic | stochastic differential equation probability density function stand basal area stand volume quantiles |
| url | https://www.mdpi.com/2227-7390/8/12/2230 |
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