Abstract
The essentials of the integrodifferential calculus of continuous martingales and local martingales in a Hilbert space are the topics of this chapter. In particular, definitions and investigations of martingales, local martingales and a Wiener process in a Hilbert space are presented and the construction of stochastic integrals with respect to these processes are given. We also derive Ito’s formula for the square of a norm of a continuous semimartingale.*
A semimartingale is sum of a martingale and a process of bounded variation.
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© 1990 Springer Science+Business Media Dordrecht
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Rozovskii, B.L. (1990). Stochastic Integration in a Hilbert Space. In: Stochastic Evolution Systems. Mathematics and Its Applications (Soviet Series), vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3830-7_2
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DOI: https://doi.org/10.1007/978-94-011-3830-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5703-5
Online ISBN: 978-94-011-3830-7
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