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..
- References:
- Cumulative probability that random walk variable exceeds given value
- From: Kelly Jones <kelly.terry.jones@gmail.com>
- Cumulative probability that random walk variable exceeds given value