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Prediction of shot noise

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Robert B. Lund ,
Ronald W. Butler  and
Robert L. Paige
Robert B. Lund*
Affiliation:
University of Georgia
Ronald W. Butler*
Affiliation:
Colorado State University
Robert L. Paige*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, The University of Georgia, Athens, GA 30602–1952. Email address: [email protected]
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523.
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523.
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Abstract

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and to arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored.

Keywords

Predictionshot noisemean squared errorsaddlepoint approximation

MSC classification

Primary: 60G25: Prediction theory
Secondary: 60G20: Generalized stochastic processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 374 - 388
Copyright
Copyright © Applied Probability Trust 1999 

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