Solving Timescales Physics Problems: Timesteps and Normal Distribution Analysis

[courtrigrad]

Hello all

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

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

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} How do we get the last part (the approximation)?

Thanks

 

[dextercioby]

The way i see it,the approximation should be
S_{M}=S_{0}e^{[\mu M(\delta t)]}

It might help if you came up with more explanation.

Daniel.

 

[courtrigrad]

yes that is correct. how do they get this? do they use taylor series?

 

[dextercioby]

No,the definition of "e"...Check one of the other threads where i showed you on a similar problem...

Daniel.