Unformatted text preview: CHAPTER 23. Recognizing a Brownian Motion 237 so both B1 and B2 are Brownian motions. Furthermore, dB1 dB2 = p 1 1,
1, 2 dW1 dW2 ,
2 dW1 dW1 dt , dt = 0: We can now apply an Extension of Levy’s Theorem that says that Brownian motions with zero
cross-variation are independent, to conclude that B1 ; B2 are independent Brownians. ...
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- Fall '15
- Brownian Motion, Brownian motions, Brownians