A Practical Introduction to Stochastic Differential Equations in Mathematical Biology

Edward Allen (June 20, 2012)

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Properties of the Wiener process are reviewed and stochastic integration is explained. Stochastic di€erential equations are introduced and some of their properties
are described. Equivalence of SDE systems is explained. Commonly used numerical
procedures are discussed for computationally solving systems of stochastic di€erential
equations. A procedure is described for deriving It†o stochastic di€erential equations
from associated discrete stochastic models for randomly-varying problems in biology.
The SDEs are derived from basic principles, i.e., from the changes in the system which
occur in a small time interval. Several examples illustrate the procedure. In particular, stochastic di€erential equations are derived for predator-prey, competition, and
epidemic problems.