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Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

Let 𝔽 F be a filtration andτbe a random time. Let 𝔾 G be the progressive enlargement of 𝔽 F withτ. We study the following formula, called the optional splitting formula: For any 𝔾 G-optional processY, there exists an 𝔽 F-optional processY′ and a function Y′′ defined on [0,∞] × (ℝ+ × Ω) being [ 0 , ] 𝒪 ( 𝔽 ) ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y = Y ' 1 [ 0 , τ ) + Y ' ' ( τ ) 1 [ τ , ) . Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random timesτ1,...,τk). We are interested in this formula because of its fundamental role in many...

Orbit coupling

Hans-Otto Georgii (1997)

Annales de l'I.H.P. Probabilités et statistiques

Ordered random walks.

Eichelsbacher, Peter, König, Wolfgang (2008)

Electronic Journal of Probability [electronic only]

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