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Ambit processes and stochastic partial differential equations. (English) Zbl 1239.91188
Di Nunno, Giulia (ed.) et al., Advanced mathematical methods for finance. Berlin: Springer (ISBN 978-3-642-18411-6/hbk; 978-3-642-18412-3/ebook). 35-74 (2011).
An Ambit process is a time-space stochastic field \(Y_t(x)\), called an ambit field, along a curve, where the ambit field \(Y_t(x)\) is typically a stochastic integral with respect to Lévy bases. It has potentially use in turbulence and finance modeling. In this paper the relationship between the ambit field and the SPDE of Walsh’s type or Lévy’s type are exploited.
For the entire collection see [Zbl 1211.91008].

MSC:
91G80 Financial applications of other theories
60H05 Stochastic integrals
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H40 White noise theory
60G57 Random measures
60G60 Random fields
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