When is an Ito process a diffusion - Quant版

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Quant版 - When is an Ito process a diffusion

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Q***5
发帖数: 994

I'm reading Oksendal's Stochastic Differential Equation,
http://books.google.com/books?id=kXw9hB4EEpUC&lpg=PP1&dq=oksend
Theorem 8.4.3, it seems that in the proof of sufficiency, only E^x(v v^t| N_
t) = \sigma \sigma^T(Y_t^x) is needed. This means that, all other conditions
hold,
E^x(v v^t| N_t) = \sigma \sigma^T(Y_t^x) implies that
v v^t( t,w) = \sigma \sigma^T(Y_t^x (w)), a little bit surprising, isn't it?
Can some experts of Stochastic process confirm?
Thanks

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