Summary
Let (Ω,ℐ, P) be a measurable space, and {ℐ t} be a filtration on (Ω,ℐ). Then, given a fixed honest timeL a new filtrationG t} is defined, the smallest containing {ℐ t} and for whichL is a stopping time, and the martingales, semimartingales and stopping times of this new filtration are characterised.
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Barlow, M.T. Study of a filtration expanded to include an honest time. Z. Wahrscheinlichkeitstheorie verw Gebiete 44, 307–323 (1978). https://doi.org/10.1007/BF01013194
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DOI: https://doi.org/10.1007/BF01013194