Abstract
We assume, as in previous chapters, that we are working on a probability space \((\varOmega,\mathcal{F},P)\) which has a filtration \(\{\mathcal{F}_{t}\}_{t\in [0,\infty ]}\) satisfying the usual conditions and, for simplicity, \(\mathcal{F}_{\infty } =\bigvee _{t<\infty }\mathcal{F}_{t}\). Furthermore, indistinguishable processes will be identified, so that when we speak of a process, we really mean an equivalence class of indistinguishable processes. When we speak of a martingale, we shall invariably mean its càdlàg version.
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References
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Cohen, S.N., Elliott, R.J. (2015). The Structure of Square Integrable Martingales. In: Stochastic Calculus and Applications. Probability and Its Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-2867-5_10
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DOI: https://doi.org/10.1007/978-1-4939-2867-5_10
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