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The Ito calculus: a vector-integral approach

Abstract:

The Itô calculus is the theory of stochastic integrals ∫t0 Xu dSu, where S is a semimartingale, and X is a suitable previsible process. The approach most commonly given in the literature is the ‘Strasbourg approach’, in which S is taken first to be an L2-martingale, and an L2-isometry is used to define the infegral. Then localization and pathwise Stieltjes integration are used to extend to the case when § is a semimartingale. I...

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Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Catherine's College
Role:
Author

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Supervisor
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Name:
Science and Engineering Research Council
Funder identifier:
http://dx.doi.org/10.13039/501100005049
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Deposit date:
2023-05-17

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