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Timescales physics problem

  1. Jan 27, 2005 #1
    Hello all

    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 :smile:
     
    Last edited: Jan 27, 2005
  2. jcsd
  3. Jan 27, 2005 #2

    dextercioby

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

    It might help if you came up with more explanation.

    Daniel.
     
  4. Jan 27, 2005 #3
    yes that is correct. how do they get this? do they use taylor series?
     
  5. Jan 27, 2005 #4

    dextercioby

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

    Daniel.
     
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