Central Limit Theorems for Conditionally Linear Random Processes.

Percy A. Pierre

Expert InsightsPublished 1971

A random process is called a linear process if it is an infinite sum of statistically independent component random processes. A particular example of a linear process is the output of a filter driven by a sequence of impulses whose times of occurrence are the times of a Poisson process. If, however, the impulses do not occur according to a Poisson process, or if the filter responses are not independent, the process is called conditionally linear. In some special cases, a linear process is passed through a low-pass filter and the output is approximately Gaussian; these are the well-known central limit theorems for linear processes. This paper presents a general and widely applicable technique for proving such theorems. Central limit theorems are obtained for the conditionally linear processes described. 33 pp. Ref. (See also RM-6013.) (KB)

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1971
  • Pages: 33
  • Document Number: P-4650

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Pierre, Percy A., Central Limit Theorems for Conditionally Linear Random Processes. Santa Monica, CA: RAND Corporation, 1971. https://www.rand.org/pubs/papers/P4650.html.
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