Show weak existence holds under the hypotheses of Proposition 25.3. Show weak existence holds under the hypotheses of Proposition 25.4. Here is an example of an SDE where weak uniqueness does not...

Show weak existence holds under the hypotheses of Proposition 25.3.

Show weak existence holds under the hypotheses of Proposition 25.4.

Here is an example of an SDE where weak uniqueness does not hold. Suppose W is a one dimensional Brownian motion and
  Find two solutions to

that are not equal in law