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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

## From Diffusions to Semimartingales

*Yacine Aïıt-Sahalia and Jean Jacod*

### in High-Frequency Financial Econometrics

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161433
- eISBN:
- 9781400850327
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161433.003.0001
- Subject:
- Economics and Finance, Econometrics

This chapter presents a quick review of the theory of semimartingales, which are processes for which statistical methods are considered in this book. Topics covered include diffusions, Lévy ... More

## Lévy Processes and Benfordʼs Law

*Klaus Schürger*

### in Benford's Law: Theory and Applications

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691147611
- eISBN:
- 9781400866595
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147611.003.0006
- Subject:
- Mathematics, Probability / Statistics

This chapter examines Lévy processes (LPs). These processes can be thought of as random walks in continuous time, having independent and stationary increments, with the assumption that the ... 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

## High-Frequency Observations: Identifiability and Asymptotic Efficiency

*Yacine Aïıt-Sahalia and Jean Jacod*

### in High-Frequency Financial Econometrics

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161433
- eISBN:
- 9781400850327
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161433.003.0005
- Subject:
- Economics and Finance, Econometrics

This chapter starts with a brief reminder about a number of concepts and results which pertain to classical statistical models, without specific reference to stochastic processes. It then introduces ... More

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