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strong solution and weak solution of SDE
I have a question about the strong and weak solution of a general SDE regarding X_t.Are the following statements correct?1. As a strong solution, X_t is adapted to the filtration generated bythe Brownian motion B_t (with x_0) appearing in the SDE? 2. As a weak solution, X_t is adapted to the filtration generated byanother Browian motion \bar{B}_t (with x_0)?3. The filtration in the strong solution is contained in thethe filtration in the weak solution. In other words, the constructionof a weak solution has used some extra information besides theoriginal BM.Thanks.