tailieunhanh - Stochastic modeling of the number of trees and the number of felled trees in selection stands

This paper solves the problem of forecasting the number of trees in the selection stands predicted for harvesting in a future period, so that the present resource of the number of trees is sustained. This is achieved by stochastic modeling of the number of trees and the number of felled trees and by solving the partial differential equation. | Yugoslav Journal of Operations Research 14 (2004), Number 1, 57-64 STOCHASTIC MODELING OF THE NUMBER OF TREES AND THE NUMBER OF FELLED TREES IN SELECTION STANDS* Slobodanka S. MITROVIĆ Faculty of Forestry University of Belgrade Belgrade, Serbia and Montenegro Received: July 2002 / Accepted: September 2003 Abstract: This paper solves the problem of forecasting the number of trees in the selection stands predicted for harvesting in a future period, so that the present resource of the number of trees is sustained. This is achieved by stochastic modeling of the number of trees and the number of felled trees and by solving the partial differential equation. Keywords: Random walk, Itô´s lemma, lognormal distribution, Itô´s stochastic differential equation, partial differential equation. 1. INTRODUCTION The number of trees in selection stands naturally increases in time. If the conditions were ideal, if there were no natural or artificial (due to an anthropogenic impact) removals of trees, the increase would be exponential in the time from t0 to t, . the dependence would be: µ (t – t0) x(t) = x0 · e (1) where x(t) is the number of trees in the selection stand per hectare depending on time t; µ is the factor of constant growth, x0 is the initial number of trees in the stand at the moment t0 . Let S(x,t) be the number of felled trees, . the planned impact of the anthropogenic factor on the number of trees x in the selection stand. There is a problem how to organise and limit the number of trees for felling in a time period t = T, without * 2000 Mathematics Subject Classification: 60H15, 35Q80, 91B76. 58 S. Mitrović / Stochastic Modeling of the Number of Trees disturbing the present resources. In other words, the question is what capacity of the number of trees in the selection stand can be counted on and planned for harvesting at a definite future moment, so as to maintain the present number of trees in the stand. The significance of the problem is manifold:

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