Use properties of the Brownian motion to show that (Wx Wk-1+p)at WR-1)at) (Wkar – Wck-1+p)at) = At /p(1 – p)Z4Z¢ W(K-1+p)At) = At Vp(1 – p)Z¢Z¢ (k-1)At - (6.61) where Z and Z each have a standard normal distribution and Zp and Z are independent random variables. (Note that the symbol d means "has the same distribution as.") Use this and the law of large numbers to argue that limn->00 Bn = 0. -n→∞
Use properties of the Brownian motion to show that (Wx Wk-1+p)at WR-1)at) (Wkar – Wck-1+p)at) = At /p(1 – p)Z4Z¢ W(K-1+p)At) = At Vp(1 – p)Z¢Z¢ (k-1)At - (6.61) where Z and Z each have a standard normal distribution and Zp and Z are independent random variables. (Note that the symbol d means "has the same distribution as.") Use this and the law of large numbers to argue that limn->00 Bn = 0. -n→∞
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Transcribed Image Text:Use properties of the Brownian motion to show that
At / p(1 – p)Z¢Z#
(6.61)
where Z and Z each have a standard normal distribution and Zp
and Z are independent random variables. (Note that the symbol
W(k-1+p)At – W{x-1)a!) (Wkat
W(k-1+p)At
d
- means "has the same distribution as.") Use this and the law of
large numbers to argue that lim,→00 Bn
0.
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