Difference between revisions of "Stochastic point process with limited memory"
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| + | $#C+1 = 5 : ~/encyclopedia/old_files/data/S090/S.0900180 Stochastic point process with limited memory | ||
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| − | in which the intervals | + | A [[Stochastic point process|stochastic point process]] defined by a sequence of random variables $ \{ t _ {i} \} $, |
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| + | $$ | ||
| + | {} \dots < t _ {-} 1 < t _ {0} \leq 0 < t _ {1} < t _ {2} < \dots , | ||
| + | $$ | ||
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| + | 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|Renewal theory]]), in which the $ s _ {i} $( | ||
| + | $ i \neq 0 $) | ||
| + | are independent identically-distributed random variables. | ||
Latest revision as of 08:23, 6 June 2020
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=48855
Stochastic point process with limited memory. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_point_process_with_limited_memory&oldid=48855
This article was adapted from an original article by Yu.K. Belyaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article