Ambit Processes and Stochastic Partial Differential Equations

CREATES Research Paper 2010-17

37 Pages Posted: 3 May 2010

See all articles by Ole E. Barndorff-Nielsen

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences

Fred Espen Benth

University of Oslo

Almut Veraart

Imperial College London; CREATES

Date Written: April 29, 2010

Abstract

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.

Keywords: Ambit processes, stochastic partial differential equations, Lévy bases, Lévy noise, Walsh theory of martingale measures, turbulence, finance

JEL Classification: C0, C1, C5

Suggested Citation

Barndorff-Nielsen, Ole E. and Benth, Fred Espen and Veraart, Almut, Ambit Processes and Stochastic Partial Differential Equations (April 29, 2010). CREATES Research Paper 2010-17, Available at SSRN: https://ssrn.com/abstract=1597697 or http://dx.doi.org/10.2139/ssrn.1597697

Ole E. Barndorff-Nielsen (Contact Author)

University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )

Ny Munkegade
Aarhus, DK 8000
Denmark

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Almut Veraart

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ

CREATES ( email )

Aarhus University
DK-8000 Aarhus C
Denmark

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