
244 Modeling and Inverse Problems in the Presence of Uncertainty
7.2 Stochastic Differential Equations
In this section, we consider stochastic differential equations (recall that
they are differential equations driven by white noise) with particular focus
on the ones driven by Gaussian white noise. This type of stochastic differ-
ential equation has been extens ively studied in the literature for b oth the-
oretical and computational analysis, including e xistence and uniq ue ne ss of
solutions, numerical methods, state estimation (often called filtering) tech-
niques and stochastic control studies (e.g., see some relatively recent books
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