Range inter-event process in a symmetric birth death random walk and the detection of chaos

Pierre Vallois, Charles S. Tapiero

Research output: Contribution to journalConference articlepeer-review


This paper provides new results regarding the range inter-events process of a birth-death random walk. Motivations for determining and using the inter-range event distribution have two sources. First, the analytical results we obtain are simpler than the range process and make it easier therefore to use statistics based on the inter-range event process. Further, most of the results regarding the range process are based on long run statistical properties which limits their practical usefulness while inter-range events are by their nature `short term' statistics. Second, in many cases, data regarding amplitude change is easier to obtain and calculate than range and standard deviation processes. As a result, the predicted statistical properties of the inter-range event process can provide an analytical foundation for the development of statistical tests that may be used practically. Application to outlier detection, volatility and time series analysis discussed. Finally, results are summarized with proofs provided in another more extensive paper.

Original languageEnglish (US)
Pages (from-to)89-99
Number of pages11
JournalNeural Network World
Issue number1
StatePublished - 2000
EventPASE 2000: 7th International Workshop on Parallel Applications in Statistics and Economics 'Managing the Unexpected: Unmodeled Dynamics in Engineering and Finance' - Leuven, Belgium
Duration: Apr 2 2000Apr 5 2000

ASJC Scopus subject areas

  • Software
  • General Neuroscience
  • Hardware and Architecture
  • Artificial Intelligence


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