However something needs to be clarified about B[sub]t[/sub] and dc
B[sub]t[/sub] follows a Brownian motion in time t
You can cut equal time intervals and each interval B changes by a normal random variable with 0 mean and time length variance; each B change in a time interval has nothing to do with another B change in a different interval.
As Δt gets small, mathematicians argue the square of ΔB has a quite steady mean Δt with a negligible (higher order) variance 2*Δt[sup]2[/sup]. Hence here comes
Thus, to approach a difference of a function which involves a brownian motion B in it directly or indirectly, you have to use Taylor expansion with order 2 to capture the innegligible dB[sup]2[/sup].
thus here come the dc
o(dt) is higher order term of dt, negligible the same way we do our normal calculus. And the final formual for dc is:
Last edited by George,Y (2008-04-19 05:09:29)