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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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