Given any is independent of (and indeed Ft if the Brownian motion is defined on a filtered probability space). Proof: This is immediate from (BM.i). - The strong Markov property is a more stringent...

Given any

is independent of

(and indeed Ft if the Brownian motion is defined on a filtered probability space).

Proof: This is immediate from (BM.i). - The strong Markov property is a more stringent requirement of a stochastic process and is correspondingly more powerful and useful. To understand this idea we must here introduce the concept of a stopping time. We will reintroduce this in Chapter 3 when we discuss stopping times in more detail.