Intensity of counting processes

The intensity λ {\displaystyle \lambda } of a counting process is a measure of the rate of change of its predictable part. If a stochastic process { N ( t ) , t ≥ 0 } {\displaystyle \{N(t),t\geq 0\}} is a counting process, then it is a submartingale, and in particular its Doob-Meyer decomposition is N ( t ) = M ( t ) + Λ ( t ) {\displaystyle N(t)=M(t)+\Lambda (t)} where M ( t ) {\displaystyle M(t)} is a martingale and Λ ( t ) {\displaystyle \Lambda (t)} is a predictable increasing process.

Source: Wikipedia — Intensity of counting processes (CC BY-SA 4.0)

Intensity of counting processes

The intensity λ {\displaystyle \lambda } of a counting process is a measure of the rate of change of its predictable part. If a stochastic process { N ( t ) , t ≥ 0 } {\displaystyle \{N(t),t\geq 0\}} is a counting process, then it is a submartingale, and in particular its Doob-Meyer decomposition is N ( t ) = M ( t ) + Λ ( t ) {\displaystyle N(t)=M(t)+\Lambda (t)} where M ( t ) {\displaystyle M(t)} is a martingale and Λ ( t ) {\displaystyle \Lambda (t)} is a predictable increasing process.

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Source: Wikipedia "Intensity of counting processes" · CC BY-SA 4.0

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