Paper 2, Section II,
Part II, 2017
(a) What is a Brownian motion?
(b) Let be a Brownian motion. Show that the process , , is also a Brownian motion.
(c) Let . Show that for all (i.e. and have the same laws). Conclude that a.s.
(d) Show that .
Paper 2, Section II,
(a) What is a Brownian motion?
(b) Let be a Brownian motion. Show that the process , , is also a Brownian motion.
(c) Let . Show that for all (i.e. and have the same laws). Conclude that a.s.
(d) Show that .