Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 202 / 4 / a / Solution

A strong solution of a stochastic differential equation is an adapted process $X$ on a prescribed filtered probability space carrying a prescribed Brownian motion $W$, satisfyingalmost surely. A weak solution of a stochastic differential equation consists of a filtered probability space, a Brownian motion, and an adapted process on that space satisfying the same integral equation; the space and driving Brownian motion are part of what may be chosen.