Chapter 8: Brownian motion and martingales

Question 1

8 Properties of Brownian Motion

Answer 1

• Independent increments
• Stationary increments
• Gaussian increments
• Continuous sample paths
• B_0 = 0
• Cov(Bs, Bt) = min(s,t)
• Brownian motion is a markov process (follows from independent increment property)
• is a martingale
• returns infinitely often to 0, or any other level

Question 2

Martingale

Answer 2

A stochastic process for which its current value is the optimal estimator of its future value.