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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

## Continuous Markov process theory

*Daniel T. Gillespie and Effrosyni Seitaridou*

### in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664504
- eISBN:
- 9780191748516
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664504.003.0007
- Subject:
- Physics, Soft Matter / Biological Physics

Three years after Einstein published his groundbreaking 1905 paper on diffusion, a different analysis was published by Paul Langevin. Although it was not clearly appreciated at the time, Langevin's ... More

## Markov processes in continuous time and space

*Eric Renshaw*

### in Stochastic Population Processes: Analysis, Approximations, Simulations

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199575312
- eISBN:
- 9780191728778
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575312.003.0006
- Subject:
- Mathematics, Applied Mathematics, Mathematical Biology

Having dealt with processes in discrete space, and discrete and continuous time, this chapter investigates Markov processes in continuous space and time. It follows a natural progression through the ... More

## Empirical Evidence of Frailty

*Darrell Duffie*

### in Measuring Corporate Default Risk

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199279234
- eISBN:
- 9780191728419
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199279234.003.0007
- Subject:
- Economics and Finance, Financial Economics

This chapter provides strong evidence of missing common or correlated default risk factors, some of which may not even have been contemporaneously available. Based on this idea, it provides estimates ... More

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