I have just started studying statistics, and have no background in this field(though I have a descent enough mathematical background).
I was studying about stationary distributions and stationary processes, and the book I am reading says that
A process is stationary if the joint distribution of random variables is same irrespective of time.
Following are my doubts regarding this:-
So does this mean that distribution(not joint) of all individual random variables(Xt) remains the same, independent of time?
I concluded from this that a stationary process is a process which has a stationary joint distribution of random variables, is this correct? If yes, then I guess it also implies stationary distribution of individual random variables(each Xt)?
Lastly, it says on wikipedia page of stationary process that "a stationary process is not the same thing as a "process with a stationary distribution"". This is the whole source of my confusion. A stationary process is something whose joint probability distribution doesn't change with time, so is there a difference between a stationary distribution and a distribution which doesn't change with time?(Is independent of time)
Though I have no background of statistics, I am really eager to learn, and would be really grateful if someone could please explain in simple terms,i.e. of a beginner. Also, it'd be great if you could suggest a book which will help in understanding these concepts(specifically of stochastic modelling) easily. Thanks a ton.