Abstract
This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set.
Highlights
Stand attributes prediction has been a popular and challenging research topic in both forestry science and economics due to its importance to forest managers, governments, as well as economic stakeholders in recent years
This study focuses on the alternative nonsymetric Bertalanfy type 4-variate diffusion process which links between tree diameter, height, crown base height and crown width dynamics, and their
This paper focuses on a 4-variate Bertalanffy type stochastic differential equation (SDE) to study the tree size variables (diameter at breast height, D(t), tree height, H(t), crown base height, CH, and crown width, CW) distribution problem in forest stands
Summary
Stand attributes prediction has been a popular and challenging research topic in both forestry science and economics due to its importance to forest managers, governments, as well as economic stakeholders in recent years. Diameter at the breast height, total tree height, crown base height and crown width size dimensions (in the sequel—tree size variables), and the number of trees per hectare are substantial components of stand growth and yield models whose evolution provide details on stand development [1]. These tree size variables are the most important predictor variables for the estimation of stem volume, biomass and carbon storage in natural forests. The basic idea is to describe a system of ordinary differential equations, which specifies changes of a suitable number of tree or stand size variables via age (time) and to summarize the relevant information about the Mathematics 2019, 7, 761; doi:10.3390/math7080761 www.mdpi.com/journal/mathematics
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