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Let [tex] \delta t [/tex] be a timestep. Then the mean is equaled to [tex] \mu\delta t [/tex] where [tex] \mu [/tex] is a constant. Assuming a nornal distribution, [tex] \frac{S_{i+1}-S_{i}}{S_i} = \mu\delta t [/tex]

[tex] S_{i+1} = S_i(1 + \mu\delta t) [/tex]. Hence after M timesteps we have:

[tex] S_m = S_0(1+\mu\delta t)^M = S_0e^{Mlog(1+\mu\delta t)} \doteq S_{M}=S_{0}e^{[\mu M(\delta t)]}= S_0e^{\mu T} [/tex] How do we get the last part (the approximation)?

Thanks

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# Timescales physics problem

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