Suppose weak uniqueness holds for the one-dimensional stochastic differential equation where W is a one-dimensional Brownian motion. Suppose also that there exists a process X that is adapted to...

Suppose weak uniqueness holds for the one-dimensional stochastic differential equation

where W is a one-dimensional Brownian motion. Suppose also that there exists a process X that is adapted to the minimal augmented filtration of W with

Prove that path wise uniqueness holds for (25.8).

Chapter 26