Modeling with Stochastic Differential Equations

Abstract

Stochastic differential equations (SDEs) are increasingly prevalent in a variety of fields. They have become routine in areas like pharmacokinetics and finance. Forestry applications, on the other hand, remain uncommon. This is an accessible introduction to the basic concepts and practical use of SDEs, with an emphasis on forest growth modeling. I begin by briefly discussing dynamical system ideas, describing rates of change in a state space instead of using functions of time directly. Rates of change can be specified by finite differences, but a formulation in continuous time with differential equations is often more convenient. Rational parameter estimation necessitates a stochastic representation of the error structure. Besides observation errors, process noise or environmental variability can be important. Both sources of variability can be taken into account with stochastic differential equations. Simple examples are demonstrated using R software.