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Distributions at random events

Podgórski, Krzysztof LU and Rychlik, Igor LU (2016) In Working Papers in Statistics
Abstract
We review the generalized Rice formula approach
to deriving long-run distributions of a variety of characteristics defined at random events defined on a stochastic process. While the approach stems from the same principle originally introduced by Rice for the level crossing intensity in a random signal, we show how it generalizes to more general contexts. Firstly, we discuss events defined on random surfaces through crossing levels of possibly multivariate valued stochastic fields. Secondly, the dynamics is introduced by adding time
argument and introducing the concept of velocity measured at moving surface. Thirdly, extensions beyond the Gaussian model are shown by presenting effective models for sampling from the... (More)
We review the generalized Rice formula approach
to deriving long-run distributions of a variety of characteristics defined at random events defined on a stochastic process. While the approach stems from the same principle originally introduced by Rice for the level crossing intensity in a random signal, we show how it generalizes to more general contexts. Firstly, we discuss events defined on random surfaces through crossing levels of possibly multivariate valued stochastic fields. Secondly, the dynamics is introduced by adding time
argument and introducing the concept of velocity measured at moving surface. Thirdly, extensions beyond the Gaussian model are shown by presenting effective models for sampling from the
distribution of a non-Gaussian noise observed at instances of level crossing by a process driven by this noise. The importance of these generalization for engineering applications is illustrated through examples. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
in
Working Papers in Statistics
issue
2016:5
pages
10 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
4aa204ff-5319-4e81-a86b-b399e2fcafc6
date added to LUP
2016-09-21 11:27:15
date last changed
2016-09-21 11:27:15
@misc{4aa204ff-5319-4e81-a86b-b399e2fcafc6,
  abstract     = {We review the generalized Rice formula approach<br/>to deriving long-run distributions of a variety of characteristics defined at random events defined on a stochastic process. While the approach stems from the same principle originally introduced by Rice for the level crossing intensity in a random signal, we show how it generalizes to more general contexts. Firstly, we discuss events defined on random surfaces through crossing levels of  possibly multivariate valued stochastic fields. Secondly, the dynamics is introduced by adding time <br/>argument and introducing the concept of velocity measured at moving surface. Thirdly, extensions  beyond the Gaussian model are shown by presenting effective models for sampling from the <br/>distribution of a non-Gaussian noise observed at instances of level crossing by a process driven by this noise. The importance of these generalization for engineering applications is illustrated through examples.},
  author       = {Podgórski, Krzysztof and Rychlik, Igor},
  language     = {eng},
  number       = {2016:5},
  pages        = {10},
  publisher    = {ARRAY(0xb2909a0)},
  series       = {Working Papers in Statistics},
  title        = {Distributions at random events},
  year         = {2016},
}