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Re: Cumulative probability that random walk variable

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104935] Re: Cumulative probability that random walk variable
  • From: fd <fdimer at gmail.com>
  • Date: Fri, 13 Nov 2009 05:58:05 -0500 (EST)
  • References: <200911110928.EAA29352@smc.vnet.net> <hdgr3b$jbt$1@smc.vnet.net>

Kelly

>From what you've written I'm assuming you want the probability that a
random normal variable will exceed X (say X=2) after n samples.

Be F[x] your cumulative probability distribution for your normal
distribution, this is

F[x]=Prob{X<=x}

where X is your stochastic variable, if you consider your time to be
discrete you can use extreme value theory to calculate the probability
of exceeding X after n steps

Prob{X_n > x} = 1-F[x]^n


This might give a good enough approximation. For a truly continuous
stochastic process this would a bit more complicated as you have to
define the step size as a function of dt..






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