Convergence of numerical solution of stochastic differential equation for the self-thinning process

Abstract

For theoretical and practical analysis of the self-thinning process we use stochastic differential equation, which take the form:

dN (t) = N (t) (α - β ln N (t))dt + μN (t)dW (t), N(t₀) = N₀, t₀ ≤ t ≤ T,

where N – tree per hectare (stem/ha), t – stand age, W(t) – scalar standard Brownian motion, N₀ – not random, α, β and μ are parameters – real constants. In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. The programs for numerical simulation are written on MAPLE. The convergence of this model is explored too.