Ambit Processes and Stochastic Partial Differential Equations

Ole Barndorff-Nielsen, Fred Espen Benth () and Almut E. D. Veraart ()
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Fred Espen Benth: University of Oslo, Centre of Mathematics for Applications
Almut E. D. Veraart: Aarhus University, CREATES, School of Economics and Management

Chapter Chapter 2 in Advanced Mathematical Methods for Finance, 2011, pp 35-74 from Springer

Abstract: 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; Levy bases; Stochastic partial differential equations; White noise analysis; Martingale measures; 60H05; 60H15; 60H40; 60G57; 60G60 (search for similar items in EconPapers)
Date: 2011
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Working Paper: Ambit processes and stochastic partial differential equations (2010)
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DOI: 10.1007/978-3-642-18412-3_2

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