Comments on SODEs: A Comparison with Other Approaches
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).
KeywordsBrownian Motion Sample Path Correlation Functional Linear Manifold Brownian Noise
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