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2 results

A local proof of the Swiss Army formula of Palm calculus
Part of
- Stochastic processes
- Special processes
Takis Konstantopoulos
Journal:

Journal of Applied Probability / Volume 33 / Issue 3 / September 1996

Published online by Cambridge University Press:

14 July 2016, pp. 909-914

Print publication:

September 1996
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The so-called ‘Swiss Army formula', derived by Brémaud, seems to be a general purpose relation which includes all known relations of Palm calculus for stationary stochastic systems driven by point processes. The purpose of this article is to present a short, and rather intuitive, proof of the formula. The proof is based on the Ryll–Nardzewski definition of the Palm probability as a Radon-Nikodym derivative, which, in a stationary context, is equivalent to the Mecke definition.

Perturbation analysis of functionals of random measures
Part of
- Inference from stochastic processes
- Stochastic processes
François Baccelli, Maurice Klein, Sergei Zuyev
Journal:

Advances in Applied Probability / Volume 27 / Issue 2 / June 1995

Published online by Cambridge University Press:

01 July 2016, pp. 306-325

Print publication:

June 1995
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We use the fact that the Palm measure of a stationary random measure is invariant to phase space change to generalize the light traffic formula initially obtained for stationary processes on a line to general spaces. This formula gives a first-order expansion for the expectation of a functional of the random measure when its intensity vanishes. This generalization leads to new algorithms for estimating gradients of functionals of geometrical random processes.

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2 results

A local proof of the Swiss Army formula of Palm calculus

Perturbation analysis of functionals of random measures