Without knowing what is or knowing what the distribution of x is, if " is the definition of , I don't see how anyone can answer that question.
Do you by any chance mean
= b + where e is a zero mean independent identically distributed noise process with a variance?
If so = + a bunch of mean zero terms with variance equal to var(e)/(1-b^2). Since b^n converges to zero the series is stationary.
As you have it written is generated by repeated draws from an iid distribution and isnt really a time series.