Time invarient pdf but nonstationary process

[shifo79]

I am wondering if there exist some solution to the general stochastic differential equation (SDE) such that I get a time independent pdf(x) while the stochastic process Xt is nonstationary.. I really need some help with that..

 

[mathman]

I am not sure what you mean by a general stochastic diff. eq. However, it is possible to have a stochastic process with a constant distribution function, but where the correlation function is dependent on both values of the independent (time) variable, and not just the difference - therefore not stationary.

 

[shifo79]

OK, forget about the SDE .. can u give me example of a stochastic process such that the pdf (doesn't depend on time == > dp/dt=0) but the correlation has a time variable (nonstationary)? this will helpso much..

 

[mathman]

Gaussian process (mean=0, s.d=1) with a correl. dep. on both variables. For example f(s,t)=1/(1+|s²-t²|).

 

[shifo79]

what's f(s,t)..
can u please tell me how to compute this correlation? if the pdf has not time in it, how come time appears in the correlation function?