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.