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# Asymptotic expansions for functionals processes

Abstract : The article provides the direct approach to obtaining formulas for derivatives of functionals of point processes in rare perturbation analysis . Results are obtained for arbitrary (not necessarily stationary) point processes in $R$ and $R^d,\ d\geq 2$, under transparent conditions, close to minimal. Formulas for higher order derivatives allow to construct asymptotical expansions. The results can be useful in sensitivity analysis, in light traffic theory for queues and for computation by simulation of derivatives at positive intensity while the computation of the derivatives via statistical estimation of the functional itself and its increments usually gives poor results.
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https://hal.inria.fr/inria-00074434
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Submitted on : Wednesday, May 24, 2006 - 3:17:35 PM
Last modification on : Friday, February 4, 2022 - 3:15:09 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:17:26 PM

### Identifiers

• HAL Id : inria-00074434, version 1

### Citation

Alexander A. Borovkov. Asymptotic expansions for functionals processes. [Research Report] RR-2236, INRIA. 1994. ⟨inria-00074434⟩

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