A standard <Brownian motion> $(B_t)_{t\geq0}$ satisfies $B_0=0$ almost surely, has almost surely <continuous function>[continuous] sample paths, and has independent stationary increments such that
$$
B_t-B_s\sim N(0,t-s)
\qquad(0\leq s<t).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 201 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-201/4/a/solution