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On some concepts of infinite divisibility and their roles in turbulence, finance and quantum stochastics

Ole Eiler Barndorff-Nielsen

in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.003.0013
Subject:
Mathematics, Probability / Statistics

This chapter contains an account of contemporary Lévy theory, namely the theory of infinite divisibility, Lévy processes, Lévy bases, and so forth, which has been a very active area of research over ... More


Classical Probability Theory and Stochastic Processes

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.01
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These ... More


Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

A. C. Davison, Yadolah Dodge, and N. Wermuth (eds)

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.001.0001
Subject:
Mathematics, Probability / Statistics

Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied ... More


Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction *

Nicholas G. Polson and James G. Scott

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0017
Subject:
Mathematics, Probability / Statistics

We study the classic problem of choosing a prior distribution for a location parameter β = (β 1,…, β p ) as p grows ... More


Applications to Quantum Optical Systems

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.08
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with a presentation of continuous measurement theory on the basis of the microscopic equations of quantum electrodynamics. The emphasis lies on the derivation of the quantum ... More


Inference for models with asymmetric α -stable noise processes

Tatjana Lemke and Simon J. Godsill

in Unobserved Components and Time Series Econometrics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.003.0009
Subject:
Economics and Finance, Econometrics

This chapter begins with a simple general framework for inference in the presence of α‎-stable processes, where the stable processes are represented as conditionally Gaussian distributions, relying ... More


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