Comments on SODEs: A Comparison with Other Approaches

Part of the Stochastic Modelling and Applied Probability formerly: Applications of Mathematics book series (SMAP, volume 58)

We briefly review Kunita's generalization of the classical Itô SODEs, driven by Brownian noise. Correlation functionals for Gaussian random fields are shown to have a representation as convolutions of certain kernels with Gaussian space—time white noise (Proposition 7.1). Under a global Lipschitz assumption, it follows that Kunita's SODEs for Brownian flows are a special case of our SODEs (4.10).


Brownian Motion Sample Path Correlation Functional Linear Manifold Brownian Noise 
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© Springer Science+Business Media, LLC 2008

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