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>