Time invarient pdf but nonstationary process

  • Thread starter Thread starter shifo79
  • Start date Start date
  • Tags Tags
    Pdf Process Time
AI Thread Summary
A solution to the general stochastic differential equation (SDE) can yield a time-independent probability density function (pdf) while maintaining a nonstationary stochastic process. It is possible to have a constant distribution function with a correlation function that depends on both time variables, indicating nonstationarity. An example provided is a Gaussian process with a mean of zero and standard deviation of one, where the correlation function is defined as f(s,t) = 1/(1+|s²-t²|). The discussion raises questions about how to compute this correlation and the apparent contradiction of having a time-independent pdf alongside a time-dependent correlation function. Understanding these concepts is crucial for exploring the dynamics of stochastic processes.
shifo79
Messages
3
Reaction score
0
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..
 
Physics news on Phys.org
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.
 
OK, forget about the SDE .. can u give me example of a stochastic process such that the pdf (dosen't depend on time == > dp/dt=0) but the correlation has a time variable (nonstationary)? this will helpso much..
 
Gaussian process (mean=0, s.d=1) with a correl. dep. on both variables. For example f(s,t)=1/(1+|s2-t2|).
 
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?
 

Thread 'Off resonant driving of a MW/RF cavity'

Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
View full post »

Similar threads

I Some notes on stochastic physics
Replies
1
Views
2K
Please help me understand a definition of a covariance function
Replies
2
Views
806
I Can the Time Independent Schroedinger Equation Be Used to Find Unbound States?
Replies
41
Views
5K
I About stochastic differential equation and probability density
Replies
1
Views
2K
I Defining Characteristic Time and Distance in an Acceleration Function
Replies
10
Views
2K
I Impulsive force and simple integration
Replies
12
Views
1K
Very strange copy-paste bug in PDF document
Replies
36
Views
3K
I String theory calculation of Extremal black hole entropy problem
Replies
3
Views
3K
Courses Are mathematicians and physicists obsessed with index notation?
Replies
12
Views
1K
I To rejuvenate the plausibility of stochastic mechanics
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top