|The relatively new subject of stochastic differential equations has increasing impor-
tance in both theory and applications. The subject draws upon two main sources, prob-
ability/stochastic processes and differential equations/dynamical systems. There exists a
signifcant \culture gap"" between the corresponding research communities. The objec-
tive of the dissertation project is to present a concise yet mostly self-contained theory of
stochastic differential equations from the differential equations/dynamical systems point of
view, primarily incorporating semigroup theory and functional analysis techniques to study
the solutions. Prerequisites from probability/stochastic processes are developed as needed.
For continuous-time stochastic processes whose random variables are (Lebesgue) absolutely
continuous, the Fokker-Planck equation is employed to study the evolution of the densities,
with applications to predator-prey models with noisy coeffcients.