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5. Renewal Counting Processes

Emanuel Parzen

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Abstract

An integer-valued, or counting, process {N(t), t≥0} corresponding to a series of points distributed on the interval 0 to ∞ is said to be a renewal counting process if the inter-arrival times T1,T2,⋯ between successive points are independent identically distributed positive random variables. This chapter discusses some of the basic properties of renewal counting processes.

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An integer-valued, or counting, process {N(t), t≥0} corresponding to a series of points distributed on the interval 0 to ∞ is said to be a renewal counting process if the inter-arrival times T1,T2,⋯ between successive points are independent identically distributed positive random variables. This chapter discusses some of the basic properties of renewal counting processes.

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Available abstract

An integer-valued, or counting, process {N(t), t≥0} corresponding to a series of points distributed on the interval 0 to ∞ is said to be a renewal counting process if the inter-arrival times T1,T2,⋯ between successive points are independent identically distributed positive random variables. This chapter discusses some of the basic properties of renewal counting processes.

Key concepts: Renewal theory, Counting process, Independent and identically distributed random variables, Mathematics, Series (stratigraphy), Sequence (biology), Stochastic process, Markov renewal process

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