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Stochastic point process with limited memory

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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.

How to Cite This Entry:
Stochastic point process with limited memory. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_point_process_with_limited_memory&oldid=18883
This article was adapted from an original article by Yu.K. Belyaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article