00. S ProoE oE Step 1. Define 6 shows). For our purposes the Ito integral will be most convenient, so we will base our discussion on that from now on. 29 EXERCISES Unless otherwise stated B t denotes Brownian motion in R, B o = O. 1. Prove directly from the definition of Ito integrals that J t J t sdB. 2. 3. Check whether the following processes X t are martingales wrt. ds o (iv) X t = B 1 (t)B 2 (t), where (B 1 (t),B 2 (t)) is 2-dimensional Brownian motion. 4. 6) that Mt = B: - t is an 9l"t-martingale. 5. 6. 4. 2. 5. 7. w.
Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal
by Donald
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