A Brief Introduction to Stochastic Differential Equations
Introduction in pdf form
Introduction in ps form
Introduction
Stochastic differential equations (sdes) are used with increasing frequency in a diverse range of fields. Financial engineers use sdes as the basis of stochastic volatility models. They are used for modeling neurons in computational neuroscience and for simulating protein dynamics in computational cell biology. They have a long history in physics where they are used to model Brownian motion. In chemistry sdes arise in the study of single molecule fluorescence and they also have potential applications as computational tools for quantum chemistry. They are used in the study of seismology and hydrology and in fatigue testing in engineering. This great diversity of applications is responsible for the increasing number of available texts. Amazon currently lists 143 titles dealing with the subject of stochastic differential equations. Unfortunately, most texts develop the theory in a very formal way which obscures the essential simplicity of the ideas. This document is an attempt to present these ideas in a more direct way.
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