i'm looking at the differential equations for a geometric Brownian motion process with a rate of appreciation of alpha and volatility of sigma.
I don't understand the differential equation listed on page 473 of the manual. table 23.1
the 4th bullet:
ln X(t) / X(0) is N(ln X(0) + (alpha - 0.5sigma^2)*t , sigma^2 * t)
somehow I cant get this. more specifically why lnx(t) / x(0) with a mean inclusive of ln x(0)?
I don't understand the differential equation listed on page 473 of the manual. table 23.1
the 4th bullet:
ln X(t) / X(0) is N(ln X(0) + (alpha - 0.5sigma^2)*t , sigma^2 * t)
somehow I cant get this. more specifically why lnx(t) / x(0) with a mean inclusive of ln x(0)?
stochastic integration asm 9th edition mfe
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