Existence of moments-> Existence of distribution?

by RolandBerg
Tags: measure theory, stationarity, statistics, stochastics, time series
RolandBerg is offline
Jan14-13, 10:16 AM
P: 1
Hi all,

this might come to you as a bit silly, because normally we are used to the vice-versa question. But here is what I have: a nonlinear time-series model, for which I can derive by infinite backwards iteration the mean and a limiting bound for variance. Now I just want to say that therefore a stationary distribution must exist.

Is this true? Any deep reason why?

[Of course moments are derived in terms of the distribution in the first place, but is this the argument?]
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