Stochastic point process with limited memory

A stochastic point process defined by a sequence of random variables $ \{ t _ {i} \} $,

$$ {} \dots < t _ {-} 1 < t _ {0} \leq 0 < t _ {1} < t _ {2} < \dots , $$

in which the intervals $ s _ {i} = t _ {i+} 1 - t _ {i} $ are mutually-independent random variables. Such processes are closely related to renewal processes (see Renewal theory), in which the $ s _ {i} $( $ i \neq 0 $) are independent identically-distributed random variables.