Optional splitting formula in a progressively enlarged filtration
Shiqi Song (2014)
ESAIM: Probability and Statistics
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Let F be a filtration andbe a random time. Let G be the progressive enlargement of F with. We study the following formula, called the optional splitting formula: For any G-optional process, there exists an F-optional process and a function defined on [0∞] × (ℝ × ) being ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...