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Let X=(Xt)t≥0,Y=(Yt)t≥0X=(X_{t})_{t\ge 0},Y=(Y_{t})_{t\ge 0}X=(Xt)t≥0,Y=(Yt)t≥0 be processes on (Ω,F,P)(\Omega,\mathcal{F},P)(Ω,F,P). X,YX,YX,Y are modifications or versions of each other if ∀t≥0\forall t\ge 0∀t≥0 Xt=Yt a.s. X_{t}=Y_{t}\text{ a.s. }Xt=Yt a.s.
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